%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWW311+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 11:01:11 AM UTC 2026
% Result : Theorem 138.14s 28.19s
% Output : CNFRefutation 28.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 267
% Syntax : Number of formulae : 3078 (1888 unt; 0 typ; 0 def)
% Number of atoms : 17128 (6812 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 61457 (5846 ~;4639 |; 48 &;50119 @)
% ( 132 <=>; 673 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 545 ( 542 usr; 49 con; 0-7 aty)
% Number of variables : 12339 ( 0 ^;12309 !; 30 ?;12339 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Big__Operators_Ocomm__monoid__add__class_Osetsum,type,
c_Big__Operators_Ocomm__monoid__add__class_Osetsum: $i > $i > $i ).
thf(tp_c_Big__Operators_Ocomm__monoid__big,type,
c_Big__Operators_Ocomm__monoid__big: $i > $i > $i > $i > $i > $o ).
thf(tp_c_Big__Operators_Ocomm__monoid__mult__class_Osetprod,type,
c_Big__Operators_Ocomm__monoid__mult__class_Osetprod: $i > $i > $i ).
thf(tp_c_Big__Operators_Olattice_OInf__fin,type,
c_Big__Operators_Olattice_OInf__fin: $i > $i > $i > $i ).
thf(tp_c_Big__Operators_Olattice_OSup__fin,type,
c_Big__Operators_Olattice_OSup__fin: $i > $i > $i > $i ).
thf(tp_c_Big__Operators_Olattice__class_OInf__fin,type,
c_Big__Operators_Olattice__class_OInf__fin: $i > $i > $i ).
thf(tp_c_Big__Operators_Olattice__class_OSup__fin,type,
c_Big__Operators_Olattice__class_OSup__fin: $i > $i > $i ).
thf(tp_c_Big__Operators_Olinorder__class_OMax,type,
c_Big__Operators_Olinorder__class_OMax: $i > $i > $i ).
thf(tp_c_Big__Operators_Olinorder__class_OMin,type,
c_Big__Operators_Olinorder__class_OMin: $i > $i > $i ).
thf(tp_c_Big__Operators_Osemilattice__big,type,
c_Big__Operators_Osemilattice__big: $i > $i > $i > $o ).
thf(tp_c_COMBB,type,
c_COMBB: $i > $i > $i > $i ).
thf(tp_c_COMBC,type,
c_COMBC: $i > $i > $i > $i ).
thf(tp_c_COMBI,type,
c_COMBI: $i > $i ).
thf(tp_c_COMBK,type,
c_COMBK: $i > $i > $i ).
thf(tp_c_COMBS,type,
c_COMBS: $i > $i > $i > $i ).
thf(tp_c_Code__Numeral_OSuc__code__numeral,type,
c_Code__Numeral_OSuc__code__numeral: $i > $i ).
thf(tp_c_Code__Numeral_Ocode__numeral_Ocode__numeral__case,type,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__case: $i > $i > $i > $i > $i ).
thf(tp_c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec,type,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec: $i > $i > $i > $i > $i ).
thf(tp_c_Code__Numeral_Ocode__numeral_Ocode__numeral__size,type,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__size: $i > $i ).
thf(tp_c_Code__Numeral_Odiv__mod__code__numeral,type,
c_Code__Numeral_Odiv__mod__code__numeral: $i > $i > $i ).
thf(tp_c_Code__Numeral_Oint__of,type,
c_Code__Numeral_Oint__of: $i ).
thf(tp_c_Code__Numeral_Onat__of,type,
c_Code__Numeral_Onat__of: $i ).
thf(tp_c_Code__Numeral_Onat__of__aux,type,
c_Code__Numeral_Onat__of__aux: $i > $i > $i ).
thf(tp_c_Code__Numeral_Oof__nat,type,
c_Code__Numeral_Oof__nat: $i ).
thf(tp_c_Code__Numeral_Osubtract__code__numeral,type,
c_Code__Numeral_Osubtract__code__numeral: $i ).
thf(tp_c_Complete__Lattice_OInf__class_OInf,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i > $i ).
thf(tp_c_Complete__Lattice_OSup__class_OSup,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).
thf(tp_c_Complete__Lattice_Ocomplete__lattice__class_OINFI,type,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI: $i > $i > $i ).
thf(tp_c_Complete__Lattice_Ocomplete__lattice__class_OSUPR,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i ).
thf(tp_c_DSequence_Oempty,type,
c_DSequence_Oempty: $i > $i ).
thf(tp_c_DSequence_Osingle,type,
c_DSequence_Osingle: $i > $i ).
thf(tp_c_DSequence_Ounion,type,
c_DSequence_Ounion: $i > $i ).
thf(tp_c_Divides_Oadjust,type,
c_Divides_Oadjust: $i > $i ).
thf(tp_c_Divides_Odiv__class_Odiv,type,
c_Divides_Odiv__class_Odiv: $i > $i ).
thf(tp_c_Divides_Odiv__class_Omod,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(tp_c_Divides_Odivmod__int,type,
c_Divides_Odivmod__int: $i > $i > $i ).
thf(tp_c_Divides_Odivmod__int__rel,type,
c_Divides_Odivmod__int__rel: $i > $i > $i ).
thf(tp_c_Divides_Odivmod__nat,type,
c_Divides_Odivmod__nat: $i > $i > $i ).
thf(tp_c_Divides_Odivmod__nat__rel,type,
c_Divides_Odivmod__nat__rel: $i > $i > $i ).
thf(tp_c_Divides_OnegDivAlg,type,
c_Divides_OnegDivAlg: $i > $i > $i ).
thf(tp_c_Divides_OnegDivAlg__rel,type,
c_Divides_OnegDivAlg__rel: $i ).
thf(tp_c_Divides_OnegateSnd,type,
c_Divides_OnegateSnd: $i ).
thf(tp_c_Divides_Opdivmod,type,
c_Divides_Opdivmod: $i > $i > $i ).
thf(tp_c_Divides_OposDivAlg,type,
c_Divides_OposDivAlg: $i > $i > $i ).
thf(tp_c_Divides_OposDivAlg__rel,type,
c_Divides_OposDivAlg__rel: $i ).
thf(tp_c_Enum_Oenum__class_Oenum__all,type,
c_Enum_Oenum__class_Oenum__all: $i > $i ).
thf(tp_c_Enum_Oenum__class_Oenum__ex,type,
c_Enum_Oenum__class_Oenum__ex: $i > $i ).
thf(tp_c_Enum_Oenum__the,type,
c_Enum_Oenum__the: $i > $i > $i ).
thf(tp_c_Enum_On__lists,type,
c_Enum_On__lists: $i > $i > $i > $i ).
thf(tp_c_Enum_Oproduct,type,
c_Enum_Oproduct: $i > $i > $i > $i > $i ).
thf(tp_c_Enum_Osublists,type,
c_Enum_Osublists: $i > $i > $i ).
thf(tp_c_Equiv__Relations_Ocongruent,type,
c_Equiv__Relations_Ocongruent: $i > $i > $i > $i > $o ).
thf(tp_c_Equiv__Relations_Ocongruent2,type,
c_Equiv__Relations_Ocongruent2: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Equiv__Relations_Oequiv,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
thf(tp_c_Equiv__Relations_Oequivp,type,
c_Equiv__Relations_Oequivp: $i > $i > $o ).
thf(tp_c_Equiv__Relations_Opart__equivp,type,
c_Equiv__Relations_Opart__equivp: $i > $i > $o ).
thf(tp_c_Equiv__Relations_Oquotient,type,
c_Equiv__Relations_Oquotient: $i > $i ).
thf(tp_c_Finite__Set_Ocard,type,
c_Finite__Set_Ocard: $i > $i ).
thf(tp_c_Finite__Set_Ofinite,type,
c_Finite__Set_Ofinite: $i > $i ).
thf(tp_c_Finite__Set_Ofold,type,
c_Finite__Set_Ofold: $i > $i > $i > $i ).
thf(tp_c_Finite__Set_Ofold1,type,
c_Finite__Set_Ofold1: $i > $i > $i ).
thf(tp_c_Finite__Set_Ofold1Set,type,
c_Finite__Set_Ofold1Set: $i > $i > $i > $i ).
thf(tp_c_Finite__Set_Ofold__graph,type,
c_Finite__Set_Ofold__graph: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Finite__Set_Ofold__image,type,
c_Finite__Set_Ofold__image: $i > $i > $i > $i ).
thf(tp_c_Finite__Set_Ofolding,type,
c_Finite__Set_Ofolding: $i > $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__idem,type,
c_Finite__Set_Ofolding__idem: $i > $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__image,type,
c_Finite__Set_Ofolding__image: $i > $i > $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__image__simple,type,
c_Finite__Set_Ofolding__image__simple: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__image__simple__idem,type,
c_Finite__Set_Ofolding__image__simple__idem: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__one,type,
c_Finite__Set_Ofolding__one: $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__one__idem,type,
c_Finite__Set_Ofolding__one__idem: $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofun__left__comm,type,
c_Finite__Set_Ofun__left__comm: $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofun__left__comm__idem,type,
c_Finite__Set_Ofun__left__comm__idem: $i > $i > $i > $o ).
thf(tp_c_FunDef_OTHE__default,type,
c_FunDef_OTHE__default: $i > $i > $i > $i ).
thf(tp_c_FunDef_Oin__rel,type,
c_FunDef_Oin__rel: $i > $i > $i > $i ).
thf(tp_c_FunDef_Ois__measure,type,
c_FunDef_Ois__measure: $i > $i > $o ).
thf(tp_c_FunDef_Omax__strict,type,
c_FunDef_Omax__strict: $i ).
thf(tp_c_FunDef_Omax__weak,type,
c_FunDef_Omax__weak: $i ).
thf(tp_c_FunDef_Omin__strict,type,
c_FunDef_Omin__strict: $i ).
thf(tp_c_FunDef_Omin__weak,type,
c_FunDef_Omin__weak: $i ).
thf(tp_c_FunDef_Opair__leq,type,
c_FunDef_Opair__leq: $i ).
thf(tp_c_FunDef_Opair__less,type,
c_FunDef_Opair__less: $i ).
thf(tp_c_FunDef_Oreduction__pair,type,
c_FunDef_Oreduction__pair: $i > $i > $o ).
thf(tp_c_FunDef_Orp__inv__image,type,
c_FunDef_Orp__inv__image: $i > $i > $i ).
thf(tp_c_Fun_Obij__betw,type,
c_Fun_Obij__betw: $i > $i > $i > $i > $i > $o ).
thf(tp_c_Fun_Ocomp,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i ).
thf(tp_c_Fun_Ofun__upd,type,
c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Fun_Oid,type,
c_Fun_Oid: $i > $i ).
thf(tp_c_Fun_Oinj__on,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(tp_c_Fun_Ooverride__on,type,
c_Fun_Ooverride__on: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Fun_Othe__inv__into,type,
c_Fun_Othe__inv__into: $i > $i > $i > $i > $i ).
thf(tp_c_Groups_Oabs__class_Oabs,type,
c_Groups_Oabs__class_Oabs: $i > $i ).
thf(tp_c_Groups_Ominus__class_Ominus,type,
c_Groups_Ominus__class_Ominus: $i > $i ).
thf(tp_c_Groups_Oone__class_Oone,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(tp_c_Groups_Oplus__class_Oplus,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
thf(tp_c_Groups_Osgn__class_Osgn,type,
c_Groups_Osgn__class_Osgn: $i > $i > $i ).
thf(tp_c_Groups_Otimes__class_Otimes,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
thf(tp_c_Groups_Ouminus__class_Ouminus,type,
c_Groups_Ouminus__class_Ouminus: $i > $i ).
thf(tp_c_Groups_Ozero__class_Ozero,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(tp_c_HOL_OAll,type,
c_HOL_OAll: $i > $i ).
thf(tp_c_HOL_OEx,type,
c_HOL_OEx: $i > $i ).
thf(tp_c_HOL_OLet,type,
c_HOL_OLet: $i > $i > $i ).
thf(tp_c_HOL_OThe,type,
c_HOL_OThe: $i > $i > $i ).
thf(tp_c_HOL_Obool_Obool__size,type,
c_HOL_Obool_Obool__size: $i > $i ).
thf(tp_c_Hilbert__Choice_OEps,type,
c_Hilbert__Choice_OEps: $i > $i > $i ).
thf(tp_c_Hilbert__Choice_Oinv__into,type,
c_Hilbert__Choice_Oinv__into: $i > $i > $i > $i > $i ).
thf(tp_c_Hoare__Mirabelle_Ohoare__derivs,type,
c_Hoare__Mirabelle_Ohoare__derivs: $i > $i > $i > $o ).
thf(tp_c_If,type,
c_If: $i > $i ).
thf(tp_c_Inductive_Ocomplete__lattice__class_Ogfp,type,
c_Inductive_Ocomplete__lattice__class_Ogfp: $i > $i > $i ).
thf(tp_c_Inductive_Ocomplete__lattice__class_Olfp,type,
c_Inductive_Ocomplete__lattice__class_Olfp: $i > $i > $i ).
thf(tp_c_Int_OAbs__Integ,type,
c_Int_OAbs__Integ: $i ).
thf(tp_c_Int_OBit0,type,
c_Int_OBit0: $i > $i ).
thf(tp_c_Int_OBit1,type,
c_Int_OBit1: $i > $i ).
thf(tp_c_Int_OInteg,type,
c_Int_OInteg: $i ).
thf(tp_c_Int_OMin,type,
c_Int_OMin: $i ).
thf(tp_c_Int_OPls,type,
c_Int_OPls: $i ).
thf(tp_c_Int_ORep__Integ,type,
c_Int_ORep__Integ: $i ).
thf(tp_c_Int_Oint__ge__less__than,type,
c_Int_Oint__ge__less__than: $i > $i ).
thf(tp_c_Int_Oint__ge__less__than2,type,
c_Int_Oint__ge__less__than2: $i > $i ).
thf(tp_c_Int_Ointrel,type,
c_Int_Ointrel: $i ).
thf(tp_c_Int_Oiszero,type,
c_Int_Oiszero: $i > $i > $o ).
thf(tp_c_Int_Onat,type,
c_Int_Onat: $i ).
thf(tp_c_Int_Onat__aux,type,
c_Int_Onat__aux: $i > $i > $i ).
thf(tp_c_Int_Onumber__class_Onumber__of,type,
c_Int_Onumber__class_Onumber__of: $i > $i ).
thf(tp_c_Int_Opred,type,
c_Int_Opred: $i > $i ).
thf(tp_c_Int_Oring__1__class_OInts,type,
c_Int_Oring__1__class_OInts: $i > $i ).
thf(tp_c_Int_Oring__1__class_Oof__int,type,
c_Int_Oring__1__class_Oof__int: $i > $i ).
thf(tp_c_Int_Osucc,type,
c_Int_Osucc: $i > $i ).
thf(tp_c_Lattices_Osemilattice__inf__class_Oinf,type,
c_Lattices_Osemilattice__inf__class_Oinf: $i > $i ).
thf(tp_c_Lattices_Osemilattice__sup__class_Osup,type,
c_Lattices_Osemilattice__sup__class_Osup: $i > $i ).
thf(tp_c_Lazy__Sequence_Oanamorph,type,
c_Lazy__Sequence_Oanamorph: $i > $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Oappend,type,
c_Lazy__Sequence_Oappend: $i > $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Obind,type,
c_Lazy__Sequence_Obind: $i > $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Oempty,type,
c_Lazy__Sequence_Oempty: $i > $i ).
thf(tp_c_Lazy__Sequence_Oflat,type,
c_Lazy__Sequence_Oflat: $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Ohb__bind,type,
c_Lazy__Sequence_Ohb__bind: $i > $i > $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Ohb__not__seq,type,
c_Lazy__Sequence_Ohb__not__seq: $i > $i ).
thf(tp_c_Lazy__Sequence_Ohb__single,type,
c_Lazy__Sequence_Ohb__single: $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Ohit__bound,type,
c_Lazy__Sequence_Ohit__bound: $i > $i ).
thf(tp_c_Lazy__Sequence_Olazy__sequence_OEmpty,type,
c_Lazy__Sequence_Olazy__sequence_OEmpty: $i > $i ).
thf(tp_c_Lazy__Sequence_Olazy__sequence_OInsert,type,
c_Lazy__Sequence_Olazy__sequence_OInsert: $i > $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case,type,
c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec,type,
c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size,type,
c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size: $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Omap,type,
c_Lazy__Sequence_Omap: $i > $i > $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Oproduct,type,
c_Lazy__Sequence_Oproduct: $i > $i > $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Osingle,type,
c_Lazy__Sequence_Osingle: $i > $i ).
thf(tp_c_Lazy__Sequence_Osmall__lazy_H,type,
c_Lazy__Sequence_Osmall__lazy_H: $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Osmall__lazy_H__rel,type,
c_Lazy__Sequence_Osmall__lazy_H__rel: $i ).
thf(tp_c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy,type,
c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy: $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Oyield,type,
c_Lazy__Sequence_Oyield: $i > $i ).
thf(tp_c_Lazy__Sequence_Oyieldn,type,
c_Lazy__Sequence_Oyieldn: $i > $i ).
thf(tp_c_List_Oall__interval__int,type,
c_List_Oall__interval__int: $i > $i > $i > $o ).
thf(tp_c_List_Oall__interval__nat,type,
c_List_Oall__interval__nat: $i > $i > $i > $o ).
thf(tp_c_List_Oappend,type,
c_List_Oappend: $i > $i ).
thf(tp_c_List_Obutlast,type,
c_List_Obutlast: $i > $i > $i ).
thf(tp_c_List_Oconcat,type,
c_List_Oconcat: $i > $i > $i ).
thf(tp_c_List_Odistinct,type,
c_List_Odistinct: $i > $i ).
thf(tp_c_List_Odrop,type,
c_List_Odrop: $i > $i ).
thf(tp_c_List_OdropWhile,type,
c_List_OdropWhile: $i > $i > $i > $i ).
thf(tp_c_List_Oembed__list,type,
c_List_Oembed__list: $i > $i ).
thf(tp_c_List_Ofilter,type,
c_List_Ofilter: $i > $i > $i ).
thf(tp_c_List_Ofoldl,type,
c_List_Ofoldl: $i > $i > $i > $i > $i ).
thf(tp_c_List_Ofoldr,type,
c_List_Ofoldr: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Ohd,type,
c_List_Ohd: $i > $i ).
thf(tp_c_List_Oinsert,type,
c_List_Oinsert: $i > $i > $i > $i ).
thf(tp_c_List_Olast,type,
c_List_Olast: $i > $i > $i ).
thf(tp_c_List_Olenlex,type,
c_List_Olenlex: $i > $i > $i ).
thf(tp_c_List_Olex,type,
c_List_Olex: $i > $i > $i ).
thf(tp_c_List_Olexn,type,
c_List_Olexn: $i > $i > $i ).
thf(tp_c_List_Olexord,type,
c_List_Olexord: $i > $i > $i ).
thf(tp_c_List_Olinorder__class_Oinsort__insert__key,type,
c_List_Olinorder__class_Oinsort__insert__key: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Olinorder__class_Oinsort__key,type,
c_List_Olinorder__class_Oinsort__key: $i > $i > $i > $i ).
thf(tp_c_List_Olinorder__class_Osort__key,type,
c_List_Olinorder__class_Osort__key: $i > $i > $i > $i > $i ).
thf(tp_c_List_Olinorder__class_Osorted,type,
c_List_Olinorder__class_Osorted: $i > $i > $o ).
thf(tp_c_List_Olinorder__class_Osorted__list__of__set,type,
c_List_Olinorder__class_Osorted__list__of__set: $i > $i > $i ).
thf(tp_c_List_Olist_OCons,type,
c_List_Olist_OCons: $i > $i ).
thf(tp_c_List_Olist_ONil,type,
c_List_Olist_ONil: $i > $i ).
thf(tp_c_List_Olist_Olist__case,type,
c_List_Olist_Olist__case: $i > $i > $i > $i > $i ).
thf(tp_c_List_Olist_Olist__size,type,
c_List_Olist_Olist__size: $i > $i > $i > $i ).
thf(tp_c_List_Olist__all,type,
c_List_Olist__all: $i > $i > $i > $o ).
thf(tp_c_List_Olist__all2,type,
c_List_Olist__all2: $i > $i > $i > $i > $i > $o ).
thf(tp_c_List_Olist__ex,type,
c_List_Olist__ex: $i > $i > $i > $o ).
thf(tp_c_List_Olist__ex1,type,
c_List_Olist__ex1: $i > $i > $i > $o ).
thf(tp_c_List_Olist__update,type,
c_List_Olist__update: $i > $i > $i ).
thf(tp_c_List_Olistrel,type,
c_List_Olistrel: $i > $i > $i ).
thf(tp_c_List_Olistrel1,type,
c_List_Olistrel1: $i > $i > $i ).
thf(tp_c_List_Olistrelp,type,
c_List_Olistrelp: $i > $i > $i > $i > $o ).
thf(tp_c_List_Olists,type,
c_List_Olists: $i > $i > $i ).
thf(tp_c_List_Olistset,type,
c_List_Olistset: $i > $i > $i ).
thf(tp_c_List_Olistsp,type,
c_List_Olistsp: $i > $i > $i ).
thf(tp_c_List_Omap,type,
c_List_Omap: $i > $i > $i ).
thf(tp_c_List_Omaps,type,
c_List_Omaps: $i > $i > $i > $i > $i ).
thf(tp_c_List_Omeasures,type,
c_List_Omeasures: $i > $i > $i ).
thf(tp_c_List_Omember,type,
c_List_Omember: $i > $i ).
thf(tp_c_List_Omonoid__add__class_Olistsum,type,
c_List_Omonoid__add__class_Olistsum: $i > $i ).
thf(tp_c_List_Onat__list,type,
c_List_Onat__list: $i > $o ).
thf(tp_c_List_Onth,type,
c_List_Onth: $i > $i ).
thf(tp_c_List_Opartition,type,
c_List_Opartition: $i > $i > $i > $i ).
thf(tp_c_List_Oremdups,type,
c_List_Oremdups: $i > $i > $i ).
thf(tp_c_List_Oremove1,type,
c_List_Oremove1: $i > $i > $i > $i ).
thf(tp_c_List_OremoveAll,type,
c_List_OremoveAll: $i > $i > $i ).
thf(tp_c_List_Oreplicate,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(tp_c_List_Oreturn__list,type,
c_List_Oreturn__list: $i > $i ).
thf(tp_c_List_Orev,type,
c_List_Orev: $i > $i ).
thf(tp_c_List_Orotate,type,
c_List_Orotate: $i > $i > $i ).
thf(tp_c_List_Orotate1,type,
c_List_Orotate1: $i > $i ).
thf(tp_c_List_Oset,type,
c_List_Oset: $i > $i ).
thf(tp_c_List_Oset__Cons,type,
c_List_Oset__Cons: $i > $i > $i > $i ).
thf(tp_c_List_Osplice,type,
c_List_Osplice: $i > $i > $i > $i ).
thf(tp_c_List_Osublist,type,
c_List_Osublist: $i > $i > $i > $i ).
thf(tp_c_List_Otake,type,
c_List_Otake: $i > $i ).
thf(tp_c_List_OtakeWhile,type,
c_List_OtakeWhile: $i > $i > $i > $i ).
thf(tp_c_List_Otl,type,
c_List_Otl: $i > $i ).
thf(tp_c_List_Otranspose,type,
c_List_Otranspose: $i > $i > $i ).
thf(tp_c_List_Otranspose__rel,type,
c_List_Otranspose__rel: $i > $i ).
thf(tp_c_List_Oupt,type,
c_List_Oupt: $i > $i > $i ).
thf(tp_c_List_Oupto,type,
c_List_Oupto: $i > $i > $i ).
thf(tp_c_List_Oupto__rel,type,
c_List_Oupto__rel: $i ).
thf(tp_c_List_Ozip,type,
c_List_Ozip: $i > $i > $i ).
thf(tp_c_Nat_OSuc,type,
c_Nat_OSuc: $i ).
thf(tp_c_Nat_Ocompow,type,
c_Nat_Ocompow: $i > $i > $i ).
thf(tp_c_Nat_Ofunpow,type,
c_Nat_Ofunpow: $i > $i ).
thf(tp_c_Nat_Onat_Onat__case,type,
c_Nat_Onat_Onat__case: $i > $i > $i > $i > $i ).
thf(tp_c_Nat_Onat_Onat__rec,type,
c_Nat_Onat_Onat__rec: $i > $i > $i > $i ).
thf(tp_c_Nat_Onat_Onat__size,type,
c_Nat_Onat_Onat__size: $i > $i ).
thf(tp_c_Nat_Osemiring__1__class_ONats,type,
c_Nat_Osemiring__1__class_ONats: $i > $i ).
thf(tp_c_Nat_Osemiring__1__class_Oof__nat,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i ).
thf(tp_c_Nat_Osemiring__1__class_Oof__nat__aux,type,
c_Nat_Osemiring__1__class_Oof__nat__aux: $i > $i > $i > $i > $i ).
thf(tp_c_Nat_Osize__class_Osize,type,
c_Nat_Osize__class_Osize: $i > $i ).
thf(tp_c_Nat__Numeral_Oneg,type,
c_Nat__Numeral_Oneg: $i ).
thf(tp_c_Nat__Transfer_Ois__nat,type,
c_Nat__Transfer_Ois__nat: $i > $o ).
thf(tp_c_Nat__Transfer_Onat__set,type,
c_Nat__Transfer_Onat__set: $i > $o ).
thf(tp_c_Nat__Transfer_Otransfer__morphism,type,
c_Nat__Transfer_Otransfer__morphism: $i > $i > $i > $i > $o ).
thf(tp_c_Nat__Transfer_Otsub,type,
c_Nat__Transfer_Otsub: $i > $i > $i ).
thf(tp_c_New__DSequence_Oneg__bind,type,
c_New__DSequence_Oneg__bind: $i > $i > $i > $i > $i ).
thf(tp_c_New__DSequence_Oneg__decr__bind,type,
c_New__DSequence_Oneg__decr__bind: $i > $i > $i > $i > $i ).
thf(tp_c_New__DSequence_Oneg__single,type,
c_New__DSequence_Oneg__single: $i > $i > $i ).
thf(tp_c_New__DSequence_Opos__bind,type,
c_New__DSequence_Opos__bind: $i > $i > $i > $i > $i ).
thf(tp_c_New__DSequence_Opos__decr__bind,type,
c_New__DSequence_Opos__decr__bind: $i > $i > $i > $i > $i ).
thf(tp_c_New__DSequence_Opos__empty,type,
c_New__DSequence_Opos__empty: $i > $i ).
thf(tp_c_New__DSequence_Opos__map,type,
c_New__DSequence_Opos__map: $i > $i > $i > $i > $i > $i ).
thf(tp_c_New__DSequence_Opos__not__seq,type,
c_New__DSequence_Opos__not__seq: $i > $i ).
thf(tp_c_New__DSequence_Opos__single,type,
c_New__DSequence_Opos__single: $i > $i > $i ).
thf(tp_c_New__DSequence_Opos__union,type,
c_New__DSequence_Opos__union: $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Oneg__bind,type,
c_New__Random__Sequence_Oneg__bind: $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Oneg__decr__bind,type,
c_New__Random__Sequence_Oneg__decr__bind: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Oneg__map,type,
c_New__Random__Sequence_Oneg__map: $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Oneg__single,type,
c_New__Random__Sequence_Oneg__single: $i > $i ).
thf(tp_c_New__Random__Sequence_Opos__bind,type,
c_New__Random__Sequence_Opos__bind: $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Opos__decr__bind,type,
c_New__Random__Sequence_Opos__decr__bind: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Opos__empty,type,
c_New__Random__Sequence_Opos__empty: $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Opos__map,type,
c_New__Random__Sequence_Opos__map: $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Opos__not__random__dseq,type,
c_New__Random__Sequence_Opos__not__random__dseq: $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Opos__single,type,
c_New__Random__Sequence_Opos__single: $i > $i ).
thf(tp_c_New__Random__Sequence_Opos__union,type,
c_New__Random__Sequence_Opos__union: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_OAbs__Frac,type,
c_Nitpick_OAbs__Frac: $i > $i > $i ).
thf(tp_c_Nitpick_OFrac,type,
c_Nitpick_OFrac: $i ).
thf(tp_c_Nitpick_ORep__Frac,type,
c_Nitpick_ORep__Frac: $i > $i ).
thf(tp_c_Nitpick_Ocard_H,type,
c_Nitpick_Ocard_H: $i > $i > $i ).
thf(tp_c_Nitpick_Odenom,type,
c_Nitpick_Odenom: $i > $i ).
thf(tp_c_Nitpick_Ofold__graph_H,type,
c_Nitpick_Ofold__graph_H: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Nitpick_Ofrac,type,
c_Nitpick_Ofrac: $i > $i ).
thf(tp_c_Nitpick_Oint__gcd,type,
c_Nitpick_Oint__gcd: $i ).
thf(tp_c_Nitpick_Oint__lcm,type,
c_Nitpick_Oint__lcm: $i > $i > $i ).
thf(tp_c_Nitpick_Oinverse__frac,type,
c_Nitpick_Oinverse__frac: $i > $i > $i ).
thf(tp_c_Nitpick_Oless__eq__frac,type,
c_Nitpick_Oless__eq__frac: $i > $i > $i > $o ).
thf(tp_c_Nitpick_Oless__frac,type,
c_Nitpick_Oless__frac: $i > $i > $i > $o ).
thf(tp_c_Nitpick_Onat__gcd,type,
c_Nitpick_Onat__gcd: $i > $i > $i ).
thf(tp_c_Nitpick_Onat__gcd__rel,type,
c_Nitpick_Onat__gcd__rel: $i ).
thf(tp_c_Nitpick_Onat__lcm,type,
c_Nitpick_Onat__lcm: $i > $i > $i ).
thf(tp_c_Nitpick_Onorm__frac,type,
c_Nitpick_Onorm__frac: $i > $i > $i ).
thf(tp_c_Nitpick_Onorm__frac__rel,type,
c_Nitpick_Onorm__frac__rel: $i ).
thf(tp_c_Nitpick_Onum,type,
c_Nitpick_Onum: $i > $i ).
thf(tp_c_Nitpick_Onumber__of__frac,type,
c_Nitpick_Onumber__of__frac: $i > $i > $i ).
thf(tp_c_Nitpick_Oof__frac,type,
c_Nitpick_Oof__frac: $i > $i > $i > $i ).
thf(tp_c_Nitpick_Oone__frac,type,
c_Nitpick_Oone__frac: $i > $i ).
thf(tp_c_Nitpick_Opair__box_OPairBox,type,
c_Nitpick_Opair__box_OPairBox: $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Opair__box_Opair__box__case,type,
c_Nitpick_Opair__box_Opair__box__case: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Opair__box_Opair__box__rec,type,
c_Nitpick_Opair__box_Opair__box__rec: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Opair__box_Opair__box__size,type,
c_Nitpick_Opair__box_Opair__box__size: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Oplus__frac,type,
c_Nitpick_Oplus__frac: $i > $i > $i > $i ).
thf(tp_c_Nitpick_Oprod,type,
c_Nitpick_Oprod: $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Orefl_H,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(tp_c_Nitpick_Osetsum_H,type,
c_Nitpick_Osetsum_H: $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Otimes__frac,type,
c_Nitpick_Otimes__frac: $i > $i > $i > $i ).
thf(tp_c_Nitpick_Ouminus__frac,type,
c_Nitpick_Ouminus__frac: $i > $i > $i ).
thf(tp_c_Nitpick_Ounknown,type,
c_Nitpick_Ounknown: $i > $o ).
thf(tp_c_Nitpick_Owf_H,type,
c_Nitpick_Owf_H: $i > $i > $o ).
thf(tp_c_Nitpick_Ozero__frac,type,
c_Nitpick_Ozero__frac: $i > $i ).
thf(tp_c_Option_Ooption_Ooption__case,type,
c_Option_Ooption_Ooption__case: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Orderings_Obot__class_Obot,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(tp_c_Orderings_Oord_Omax,type,
c_Orderings_Oord_Omax: $i > $i > $i ).
thf(tp_c_Orderings_Oord_Omin,type,
c_Orderings_Oord_Omin: $i > $i > $i ).
thf(tp_c_Orderings_Oord__class_OLeast,type,
c_Orderings_Oord__class_OLeast: $i > $i > $i ).
thf(tp_c_Orderings_Oord__class_Oless,type,
c_Orderings_Oord__class_Oless: $i > $i ).
thf(tp_c_Orderings_Oord__class_Oless__eq,type,
c_Orderings_Oord__class_Oless__eq: $i > $i ).
thf(tp_c_Orderings_Oord__class_Omax,type,
c_Orderings_Oord__class_Omax: $i > $i ).
thf(tp_c_Orderings_Oord__class_Omin,type,
c_Orderings_Oord__class_Omin: $i > $i ).
thf(tp_c_Orderings_Oorder__class_Omono,type,
c_Orderings_Oorder__class_Omono: $i > $i > $i > $o ).
thf(tp_c_Orderings_Oorder__class_Ostrict__mono,type,
c_Orderings_Oorder__class_Ostrict__mono: $i > $i > $i > $o ).
thf(tp_c_Orderings_Otop__class_Otop,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(tp_c_Partial__Function_Oflat__lub,type,
c_Partial__Function_Oflat__lub: $i > $i > $i > $i ).
thf(tp_c_Partial__Function_Ofun__lub,type,
c_Partial__Function_Ofun__lub: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_Power_Opower_Opower,type,
c_Power_Opower_Opower: $i > $i > $i > $i ).
thf(tp_c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: $i > $i ).
thf(tp_c_Predicate_ODomainP,type,
c_Predicate_ODomainP: $i > $i > $i > $i ).
thf(tp_c_Predicate_OPowp,type,
c_Predicate_OPowp: $i > $i > $i ).
thf(tp_c_Predicate_ORangeP,type,
c_Predicate_ORangeP: $i > $i > $i > $i ).
thf(tp_c_Predicate_Oconversep,type,
c_Predicate_Oconversep: $i > $i > $i > $i ).
thf(tp_c_Predicate_Opred__comp,type,
c_Predicate_Opred__comp: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Predicate_Oreflp,type,
c_Predicate_Oreflp: $i > $i > $o ).
thf(tp_c_Predicate_Osymp,type,
c_Predicate_Osymp: $i > $i > $o ).
thf(tp_c_Predicate_Otransp,type,
c_Predicate_Otransp: $i > $i > $o ).
thf(tp_c_Product__Type_OPair,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(tp_c_Product__Type_OSigma,type,
c_Product__Type_OSigma: $i > $i > $i ).
thf(tp_c_Product__Type_Oapfst,type,
c_Product__Type_Oapfst: $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Oapsnd,type,
c_Product__Type_Oapsnd: $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Ocurry,type,
c_Product__Type_Ocurry: $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Ofst,type,
c_Product__Type_Ofst: $i > $i > $i ).
thf(tp_c_Product__Type_Ointernal__split,type,
c_Product__Type_Ointernal__split: $i > $i > $i > $i ).
thf(tp_c_Product__Type_Omap__pair,type,
c_Product__Type_Omap__pair: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Oprod_Oprod__case,type,
c_Product__Type_Oprod_Oprod__case: $i > $i > $i > $i ).
thf(tp_c_Product__Type_Oprod_Oprod__rec,type,
c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Oprod_Oprod__size,type,
c_Product__Type_Oprod_Oprod__size: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Oscomp,type,
c_Product__Type_Oscomp: $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Osnd,type,
c_Product__Type_Osnd: $i > $i > $i ).
thf(tp_c_Quickcheck_Obeyond,type,
c_Quickcheck_Obeyond: $i > $i > $i ).
thf(tp_c_Quotient_OBabs,type,
c_Quotient_OBabs: $i > $i > $i > $i > $i ).
thf(tp_c_Quotient_ORespects,type,
c_Quotient_ORespects: $i > $i > $i ).
thf(tp_c_Random_Oinc__shift,type,
c_Random_Oinc__shift: $i > $i > $i ).
thf(tp_c_Random_Oiterate,type,
c_Random_Oiterate: $i > $i > $i > $i > $i ).
thf(tp_c_Random_Olog,type,
c_Random_Olog: $i > $i > $i ).
thf(tp_c_Random_Ominus__shift,type,
c_Random_Ominus__shift: $i > $i > $i > $i ).
thf(tp_c_Random_Opick,type,
c_Random_Opick: $i > $i > $i ).
thf(tp_c_Random_Orange,type,
c_Random_Orange: $i > $i ).
thf(tp_c_Random_Oselect,type,
c_Random_Oselect: $i > $i > $i ).
thf(tp_c_Random_Oselect__weight,type,
c_Random_Oselect__weight: $i > $i > $i ).
thf(tp_c_Random__Sequence_ORandom,type,
c_Random__Sequence_ORandom: $i > $i > $i > $i > $i ).
thf(tp_c_Random__Sequence_Obind,type,
c_Random__Sequence_Obind: $i > $i > $i > $i > $i ).
thf(tp_c_Random__Sequence_Oempty,type,
c_Random__Sequence_Oempty: $i > $i > $i > $i ).
thf(tp_c_Random__Sequence_Omap,type,
c_Random__Sequence_Omap: $i > $i > $i > $i > $i ).
thf(tp_c_Random__Sequence_Osingle,type,
c_Random__Sequence_Osingle: $i > $i ).
thf(tp_c_Recdef_Osame__fst,type,
c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).
thf(tp_c_Relation_ODomain,type,
c_Relation_ODomain: $i > $i > $i ).
thf(tp_c_Relation_OField,type,
c_Relation_OField: $i > $i ).
thf(tp_c_Relation_OId,type,
c_Relation_OId: $i > $i ).
thf(tp_c_Relation_OId__on,type,
c_Relation_OId__on: $i > $i > $i ).
thf(tp_c_Relation_OImage,type,
c_Relation_OImage: $i > $i > $i > $i ).
thf(tp_c_Relation_ORange,type,
c_Relation_ORange: $i > $i > $i ).
thf(tp_c_Relation_Oantisym,type,
c_Relation_Oantisym: $i > $i > $o ).
thf(tp_c_Relation_Oconverse,type,
c_Relation_Oconverse: $i > $i > $i ).
thf(tp_c_Relation_Oinv__image,type,
c_Relation_Oinv__image: $i > $i > $i ).
thf(tp_c_Relation_Oirrefl,type,
c_Relation_Oirrefl: $i > $i > $o ).
thf(tp_c_Relation_Orefl__on,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
thf(tp_c_Relation_Orel__comp,type,
c_Relation_Orel__comp: $i > $i > $i > $i ).
thf(tp_c_Relation_Osingle__valued,type,
c_Relation_Osingle__valued: $i > $i > $i > $o ).
thf(tp_c_Relation_Osym,type,
c_Relation_Osym: $i > $i > $o ).
thf(tp_c_Relation_Ototal__on,type,
c_Relation_Ototal__on: $i > $i > $i > $o ).
thf(tp_c_Relation_Otrans,type,
c_Relation_Otrans: $i > $i > $o ).
thf(tp_c_Rings_Odvd__class_Odvd,type,
c_Rings_Odvd__class_Odvd: $i > $i ).
thf(tp_c_Rings_Oinverse__class_Odivide,type,
c_Rings_Oinverse__class_Odivide: $i > $i ).
thf(tp_c_SMT_Oz3div,type,
c_SMT_Oz3div: $i > $i > $i ).
thf(tp_c_SMT_Oz3mod,type,
c_SMT_Oz3mod: $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OatLeast,type,
c_SetInterval_Oord_OatLeast: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OatLeastAtMost,type,
c_SetInterval_Oord_OatLeastAtMost: $i > $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OatLeastLessThan,type,
c_SetInterval_Oord_OatLeastLessThan: $i > $i > $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OatMost,type,
c_SetInterval_Oord_OatMost: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OgreaterThan,type,
c_SetInterval_Oord_OgreaterThan: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OgreaterThanAtMost,type,
c_SetInterval_Oord_OgreaterThanAtMost: $i > $i > $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OgreaterThanLessThan,type,
c_SetInterval_Oord_OgreaterThanLessThan: $i > $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OlessThan,type,
c_SetInterval_Oord_OlessThan: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord__class_OatLeast,type,
c_SetInterval_Oord__class_OatLeast: $i > $i ).
thf(tp_c_SetInterval_Oord__class_OatLeastAtMost,type,
c_SetInterval_Oord__class_OatLeastAtMost: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord__class_OatLeastLessThan,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i ).
thf(tp_c_SetInterval_Oord__class_OatMost,type,
c_SetInterval_Oord__class_OatMost: $i > $i ).
thf(tp_c_SetInterval_Oord__class_OgreaterThan,type,
c_SetInterval_Oord__class_OgreaterThan: $i > $i ).
thf(tp_c_SetInterval_Oord__class_OgreaterThanAtMost,type,
c_SetInterval_Oord__class_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord__class_OgreaterThanLessThan,type,
c_SetInterval_Oord__class_OgreaterThanLessThan: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord__class_OlessThan,type,
c_SetInterval_Oord__class_OlessThan: $i > $i ).
thf(tp_c_Set_OBall,type,
c_Set_OBall: $i > $i ).
thf(tp_c_Set_OBex,type,
c_Set_OBex: $i > $i ).
thf(tp_c_Set_OCollect,type,
c_Set_OCollect: $i > $i ).
thf(tp_c_Set_OPow,type,
c_Set_OPow: $i > $i ).
thf(tp_c_Set_Oimage,type,
c_Set_Oimage: $i > $i > $i > $i ).
thf(tp_c_Set_Oinsert,type,
c_Set_Oinsert: $i > $i ).
thf(tp_c_Set_Othe__elem,type,
c_Set_Othe__elem: $i > $i > $i ).
thf(tp_c_Set_Ovimage,type,
c_Set_Ovimage: $i > $i > $i > $i ).
thf(tp_c_Sum__Type_OPlus,type,
c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).
thf(tp_c_Transitive__Closure_Ortrancl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(tp_c_Transitive__Closure_Otrancl,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(tp_c_Typedef_Otype__definition,type,
c_Typedef_Otype__definition: $i > $i > $i > $i > $i > $o ).
thf(tp_c_Wellfounded_Oacc,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(tp_c_Wellfounded_Oaccp,type,
c_Wellfounded_Oaccp: $i > $i > $i ).
thf(tp_c_Wellfounded_Oacyclic,type,
c_Wellfounded_Oacyclic: $i > $i > $o ).
thf(tp_c_Wellfounded_Ofinite__psubset,type,
c_Wellfounded_Ofinite__psubset: $i > $i ).
thf(tp_c_Wellfounded_Oless__than,type,
c_Wellfounded_Oless__than: $i ).
thf(tp_c_Wellfounded_Olex__prod,type,
c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).
thf(tp_c_Wellfounded_Omax__ext,type,
c_Wellfounded_Omax__ext: $i > $i > $i ).
thf(tp_c_Wellfounded_Omax__extp,type,
c_Wellfounded_Omax__extp: $i > $i > $i > $i > $o ).
thf(tp_c_Wellfounded_Omeasure,type,
c_Wellfounded_Omeasure: $i > $i ).
thf(tp_c_Wellfounded_Omin__ext,type,
c_Wellfounded_Omin__ext: $i > $i > $i ).
thf(tp_c_Wellfounded_Omlex__prod,type,
c_Wellfounded_Omlex__prod: $i > $i > $i > $i ).
thf(tp_c_Wellfounded_Opred__nat,type,
c_Wellfounded_Opred__nat: $i ).
thf(tp_c_Wellfounded_Owf,type,
c_Wellfounded_Owf: $i > $i > $o ).
thf(tp_c_Wellfounded_OwfP,type,
c_Wellfounded_OwfP: $i > $i > $o ).
thf(tp_c_fFalse,type,
c_fFalse: $i ).
thf(tp_c_fNot,type,
c_fNot: $i ).
thf(tp_c_fTrue,type,
c_fTrue: $i ).
thf(tp_c_fconj,type,
c_fconj: $i ).
thf(tp_c_fdisj,type,
c_fdisj: $i ).
thf(tp_c_fequal,type,
c_fequal: $i ).
thf(tp_c_fimplies,type,
c_fimplies: $i ).
thf(tp_c_member,type,
c_member: $i > $i ).
thf(tp_class_Complete__Lattice_Ocomplete__lattice,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(tp_class_Divides_Oring__div,type,
class_Divides_Oring__div: $i > $o ).
thf(tp_class_Divides_Osemiring__div,type,
class_Divides_Osemiring__div: $i > $o ).
thf(tp_class_Enum_Oenum,type,
class_Enum_Oenum: $i > $o ).
thf(tp_class_Fields_Ofield,type,
class_Fields_Ofield: $i > $o ).
thf(tp_class_Fields_Ofield__inverse__zero,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
thf(tp_class_Fields_Olinordered__field,type,
class_Fields_Olinordered__field: $i > $o ).
thf(tp_class_Fields_Olinordered__field__inverse__zero,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
thf(tp_class_Finite__Set_Ofinite,type,
class_Finite__Set_Ofinite: $i > $o ).
thf(tp_class_Groups_Oab__group__add,type,
class_Groups_Oab__group__add: $i > $o ).
thf(tp_class_Groups_Oab__semigroup__add,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Oab__semigroup__mult,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
thf(tp_class_Groups_Oabs__if,type,
class_Groups_Oabs__if: $i > $o ).
thf(tp_class_Groups_Ocancel__ab__semigroup__add,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Ocancel__semigroup__add,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
thf(tp_class_Groups_Ocomm__monoid__add,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(tp_class_Groups_Ocomm__monoid__mult,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
thf(tp_class_Groups_Ogroup__add,type,
class_Groups_Ogroup__add: $i > $o ).
thf(tp_class_Groups_Olinordered__ab__group__add,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(tp_class_Groups_Olinordered__ab__semigroup__add,type,
class_Groups_Olinordered__ab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Ominus,type,
class_Groups_Ominus: $i > $o ).
thf(tp_class_Groups_Omonoid__add,type,
class_Groups_Omonoid__add: $i > $o ).
thf(tp_class_Groups_Omonoid__mult,type,
class_Groups_Omonoid__mult: $i > $o ).
thf(tp_class_Groups_Oone,type,
class_Groups_Oone: $i > $o ).
thf(tp_class_Groups_Oordered__ab__group__add,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
thf(tp_class_Groups_Oordered__ab__group__add__abs,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
thf(tp_class_Groups_Oordered__ab__semigroup__add,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Oordered__ab__semigroup__add__imp__le,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
thf(tp_class_Groups_Oordered__cancel__ab__semigroup__add,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Oordered__comm__monoid__add,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
thf(tp_class_Groups_Osemigroup__add,type,
class_Groups_Osemigroup__add: $i > $o ).
thf(tp_class_Groups_Osgn__if,type,
class_Groups_Osgn__if: $i > $o ).
thf(tp_class_Groups_Ouminus,type,
class_Groups_Ouminus: $i > $o ).
thf(tp_class_Groups_Ozero,type,
class_Groups_Ozero: $i > $o ).
thf(tp_class_Int_Onumber,type,
class_Int_Onumber: $i > $o ).
thf(tp_class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
thf(tp_class_Int_Oring__char__0,type,
class_Int_Oring__char__0: $i > $o ).
thf(tp_class_Lattices_Oab__semigroup__idem__mult,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
thf(tp_class_Lattices_Oboolean__algebra,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(tp_class_Lattices_Obounded__lattice,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(tp_class_Lattices_Obounded__lattice__bot,type,
class_Lattices_Obounded__lattice__bot: $i > $o ).
thf(tp_class_Lattices_Obounded__lattice__top,type,
class_Lattices_Obounded__lattice__top: $i > $o ).
thf(tp_class_Lattices_Odistrib__lattice,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(tp_class_Lattices_Olattice,type,
class_Lattices_Olattice: $i > $o ).
thf(tp_class_Lattices_Osemilattice__inf,type,
class_Lattices_Osemilattice__inf: $i > $o ).
thf(tp_class_Lattices_Osemilattice__sup,type,
class_Lattices_Osemilattice__sup: $i > $o ).
thf(tp_class_Lazy__Sequence_Osmall__lazy,type,
class_Lazy__Sequence_Osmall__lazy: $i > $o ).
thf(tp_class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(tp_class_Nat_Osize,type,
class_Nat_Osize: $i > $o ).
thf(tp_class_Orderings_Obot,type,
class_Orderings_Obot: $i > $o ).
thf(tp_class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
thf(tp_class_Orderings_Oord,type,
class_Orderings_Oord: $i > $o ).
thf(tp_class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
thf(tp_class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
thf(tp_class_Orderings_Otop,type,
class_Orderings_Otop: $i > $o ).
thf(tp_class_Orderings_Owellorder,type,
class_Orderings_Owellorder: $i > $o ).
thf(tp_class_Power_Opower,type,
class_Power_Opower: $i > $o ).
thf(tp_class_Rings_Ocomm__ring__1,type,
class_Rings_Ocomm__ring__1: $i > $o ).
thf(tp_class_Rings_Ocomm__semiring,type,
class_Rings_Ocomm__semiring: $i > $o ).
thf(tp_class_Rings_Ocomm__semiring__1,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(tp_class_Rings_Odivision__ring,type,
class_Rings_Odivision__ring: $i > $o ).
thf(tp_class_Rings_Odivision__ring__inverse__zero,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
thf(tp_class_Rings_Oidom,type,
class_Rings_Oidom: $i > $o ).
thf(tp_class_Rings_Oinverse,type,
class_Rings_Oinverse: $i > $o ).
thf(tp_class_Rings_Olinordered__comm__semiring__strict,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
thf(tp_class_Rings_Olinordered__idom,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(tp_class_Rings_Olinordered__ring,type,
class_Rings_Olinordered__ring: $i > $o ).
thf(tp_class_Rings_Olinordered__ring__strict,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
thf(tp_class_Rings_Olinordered__semidom,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(tp_class_Rings_Olinordered__semiring,type,
class_Rings_Olinordered__semiring: $i > $o ).
thf(tp_class_Rings_Olinordered__semiring__1,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
thf(tp_class_Rings_Olinordered__semiring__1__strict,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
thf(tp_class_Rings_Olinordered__semiring__strict,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
thf(tp_class_Rings_Omult__zero,type,
class_Rings_Omult__zero: $i > $o ).
thf(tp_class_Rings_Ono__zero__divisors,type,
class_Rings_Ono__zero__divisors: $i > $o ).
thf(tp_class_Rings_Oordered__cancel__semiring,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
thf(tp_class_Rings_Oordered__comm__semiring,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
thf(tp_class_Rings_Oordered__ring,type,
class_Rings_Oordered__ring: $i > $o ).
thf(tp_class_Rings_Oordered__ring__abs,type,
class_Rings_Oordered__ring__abs: $i > $o ).
thf(tp_class_Rings_Oordered__semiring,type,
class_Rings_Oordered__semiring: $i > $o ).
thf(tp_class_Rings_Oring,type,
class_Rings_Oring: $i > $o ).
thf(tp_class_Rings_Oring__1,type,
class_Rings_Oring__1: $i > $o ).
thf(tp_class_Rings_Oring__1__no__zero__divisors,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
thf(tp_class_Rings_Oring__no__zero__divisors,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
thf(tp_class_Rings_Osemiring,type,
class_Rings_Osemiring: $i > $o ).
thf(tp_class_Rings_Osemiring__0,type,
class_Rings_Osemiring__0: $i > $o ).
thf(tp_class_Rings_Osemiring__1,type,
class_Rings_Osemiring__1: $i > $o ).
thf(tp_class_Rings_Ozero__neq__one,type,
class_Rings_Ozero__neq__one: $i > $o ).
thf(tp_class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
thf(tp_hAPP,type,
hAPP: $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_sK10_SY2264,type,
sK10_SY2264: $i > $i > $i > $i ).
thf(tp_sK11_SY2545,type,
sK11_SY2545: $i > $i > $i > $i ).
thf(tp_sK12_SY1684,type,
sK12_SY1684: $i > $i > $i > $i > $i ).
thf(tp_sK13_SY1733,type,
sK13_SY1733: $i > $i > $i > $i > $i ).
thf(tp_sK14_SY1062,type,
sK14_SY1062: $i > $i > $i ).
thf(tp_sK15_SY2374,type,
sK15_SY2374: $i > $i > $i > $i > $i ).
thf(tp_sK16_SY2478,type,
sK16_SY2478: $i > $i > $i > $i > $i > $i ).
thf(tp_sK17_SY2491,type,
sK17_SY2491: $i > $i > $i > $i > $i > $i ).
thf(tp_sK18_SY2430,type,
sK18_SY2430: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK19_SY1066,type,
sK19_SY1066: $i > $i > $i > $i ).
thf(tp_sK1_B_G,type,
sK1_B_G: $i ).
thf(tp_sK20_SY2549,type,
sK20_SY2549: $i > $i > $i > $i ).
thf(tp_sK2_SY1802,type,
sK2_SY1802: $i > $i > $i ).
thf(tp_sK3_SY1425,type,
sK3_SY1425: $i > $i > $i ).
thf(tp_sK4_SY2341,type,
sK4_SY2341: $i > $i > $i > $i > $i ).
thf(tp_sK5_SY2146,type,
sK5_SY2146: $i > $i > $i > $i ).
thf(tp_sK6_SY2154,type,
sK6_SY2154: $i > $i > $i > $i ).
thf(tp_sK7_SY1800,type,
sK7_SY1800: $i > $i > $i ).
thf(tp_sK8_SY2542,type,
sK8_SY2542: $i > $i > $i ).
thf(tp_sK9_SY2261,type,
sK9_SY2261: $i > $i > $i > $i ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_Code__Evaluation_Oterm,type,
tc_Code__Evaluation_Oterm: $i ).
thf(tp_tc_Code__Numeral_Ocode__numeral,type,
tc_Code__Numeral_Ocode__numeral: $i ).
thf(tp_tc_HOL_Obool,type,
tc_HOL_Obool: $i ).
thf(tp_tc_Hoare__Mirabelle_Otriple,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
thf(tp_tc_Int_Oint,type,
tc_Int_Oint: $i ).
thf(tp_tc_Lazy__Sequence_Olazy__sequence,type,
tc_Lazy__Sequence_Olazy__sequence: $i > $i ).
thf(tp_tc_List_Olist,type,
tc_List_Olist: $i > $i ).
thf(tp_tc_Nat_Onat,type,
tc_Nat_Onat: $i ).
thf(tp_tc_Nitpick_Opair__box,type,
tc_Nitpick_Opair__box: $i > $i > $i ).
thf(tp_tc_Option_Ooption,type,
tc_Option_Ooption: $i > $i ).
thf(tp_tc_Product__Type_Ounit,type,
tc_Product__Type_Ounit: $i ).
thf(tp_tc_fun,type,
tc_fun: $i > $i > $i ).
thf(tp_tc_prod,type,
tc_prod: $i > $i > $i ).
thf(tp_tc_sum,type,
tc_sum: $i > $i > $i ).
thf(tp_v_G_H,type,
v_G_H: $i ).
thf(tp_v_ts,type,
v_ts: $i ).
thf(1,axiom,
! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) )
| ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ V_Q_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__3) ).
thf(2,axiom,
! [V_P_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__2) ).
thf(3,axiom,
! [V_Q_2: $i,V_P_2: $i] :
( ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__1) ).
thf(4,axiom,
! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_P_2 )
| ( hBOOL @ V_Q_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__3) ).
thf(5,axiom,
! [V_P_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__2) ).
thf(6,axiom,
! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__1) ).
thf(7,axiom,
! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_Q_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__3) ).
thf(8,axiom,
! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_P_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__2) ).
thf(9,axiom,
! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ V_P_2 )
| ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__1) ).
thf(10,axiom,
! [V_P_2: $i] :
( ~ ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__2) ).
thf(11,axiom,
! [V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) )
| ~ ( hBOOL @ V_P_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
thf(12,axiom,
hBOOL @ c_fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fTrue__1) ).
thf(13,axiom,
~ ( hBOOL @ c_fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fFalse__1) ).
thf(14,axiom,
! [V_y_2: $i,V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(15,axiom,
! [V_y_2: $i,V_x_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) )
| ( V_x_2 = V_y_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(16,axiom,
! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_c @ T_d @ T_b ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
thf(17,axiom,
! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_c @ T_d @ T_b ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ V_Q_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
thf(18,axiom,
! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_c @ T_b @ T_d ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ V_P_2 @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
thf(19,axiom,
! [V_Q: $i,V_P: $i,T_b: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ T_a @ T_b ) @ V_P ) @ V_Q )
= V_P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
thf(20,axiom,
! [V_P: $i,T_a: $i] :
( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
= V_P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
thf(63,axiom,
! [T_1: $i] : ( class_Nat_Osize @ ( tc_Hoare__Mirabelle_Otriple @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Hoare____Mirabelle__Otriple__Nat_Osize) ).
thf(82,axiom,
class_Nat_Osize @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Nat_Osize) ).
thf(83,axiom,
class_Enum_Oenum @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Enum_Oenum) ).
thf(84,axiom,
class_Groups_Ominus @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
thf(85,axiom,
class_Groups_Ouminus @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
thf(86,axiom,
class_Orderings_Obot @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
thf(87,axiom,
class_Orderings_Oord @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
thf(88,axiom,
class_Orderings_Otop @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
thf(89,axiom,
class_Orderings_Oorder @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
thf(90,axiom,
class_Lattices_Olattice @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
thf(91,axiom,
class_Finite__Set_Ofinite @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
thf(92,axiom,
class_Orderings_Opreorder @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
thf(93,axiom,
class_Lattices_Oboolean__algebra @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
thf(94,axiom,
class_Lattices_Odistrib__lattice @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Odistrib__lattice) ).
thf(95,axiom,
class_Lattices_Osemilattice__inf @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
thf(96,axiom,
class_Lattices_Osemilattice__sup @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).
thf(97,axiom,
class_Lattices_Obounded__lattice__bot @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
thf(98,axiom,
class_Lattices_Obounded__lattice__top @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__top) ).
thf(99,axiom,
class_Complete__Lattice_Ocomplete__lattice @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice) ).
thf(218,axiom,
! [T_1: $i,T_2: $i] :
( ( ( class_Enum_Oenum @ T_2 )
& ( class_Enum_Oenum @ T_1 ) )
=> ( class_Enum_Oenum @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Enum_Oenum) ).
thf(219,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Groups_Ominus @ T_1 )
=> ( class_Groups_Ominus @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
thf(220,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Groups_Ouminus @ T_1 )
=> ( class_Groups_Ouminus @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
thf(221,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Obot @ T_1 )
=> ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).
thf(222,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oord @ T_1 )
=> ( class_Orderings_Oord @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(223,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Otop @ T_1 )
=> ( class_Orderings_Otop @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).
thf(224,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ T_1 )
=> ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
thf(225,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olattice @ T_1 )
=> ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).
thf(226,axiom,
! [T_1: $i,T_2: $i] :
( ( ( class_Finite__Set_Ofinite @ T_2 )
& ( class_Finite__Set_Ofinite @ T_1 ) )
=> ( class_Finite__Set_Ofinite @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).
thf(227,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ T_1 )
=> ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
thf(228,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Oboolean__algebra @ T_1 )
=> ( class_Lattices_Oboolean__algebra @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
thf(229,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Odistrib__lattice @ T_1 )
=> ( class_Lattices_Odistrib__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Odistrib__lattice) ).
thf(234,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ T_1 )
=> ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(235,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Obounded__lattice @ T_1 )
=> ( class_Lattices_Obounded__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).
thf(236,axiom,
class_Lattices_Obounded__lattice @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice) ).
thf(315,axiom,
! [V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ T_b @ V_R_2 ) @ V_x_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Respects__def) ).
thf(404,axiom,
! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Opart__equivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_z_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_part__equivp__transp) ).
thf(405,axiom,
! [V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Opart__equivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_part__equivp__symp) ).
thf(406,axiom,
! [V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Opart__equivp @ T_b @ V_R_2 )
<=> ( ? [B_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_x ) )
& ! [B_x: $i,B_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_y ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_x ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_y ) @ B_y ) )
& ( ( hAPP @ V_R_2 @ B_x )
= ( hAPP @ V_R_2 @ B_y ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_part__equivp__def) ).
thf(441,axiom,
! [V_y_2: $i,V_x_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Predicate_Osymp @ T_b @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_y_2 ) @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sympE) ).
thf(444,axiom,
! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Predicate_Otransp @ T_b @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_y_2 ) @ V_z_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpE) ).
thf(559,axiom,
! [V_b_2: $i,V_a_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_b_2 ) @ V_a_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversepD) ).
thf(560,axiom,
! [T_c: $i,T_b: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_b_2 ) @ V_a_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversep_Ointros) ).
thf(561,axiom,
! [V_a1_2: $i,V_a2_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_a2_2 ) @ V_a1_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ V_a2_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversep_Oequations) ).
thf(562,axiom,
! [V_b_2: $i,V_a_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_a_2 ) @ V_b_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_b_2 ) @ V_a_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversep__iff) ).
thf(720,axiom,
! [V_xs: $i,T_a: $i] :
( ( hAPP @ ( c_List_Orev @ T_a ) @ ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs ) )
= V_xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
thf(721,axiom,
! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
= V_ys_2 )
<=> ( V_xs_2
= ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__swap) ).
thf(722,axiom,
! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
= ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) )
<=> ( V_xs_2 = V_ys_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__is__rev__conv) ).
thf(972,axiom,
! [V_l_2: $i,V_k_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_k_2 )
= ( hAPP @ c_Code__Numeral_Onat__of @ V_l_2 ) )
<=> ( V_k_2 = V_l_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Code__Numeral_Onat__of__inject) ).
thf(973,axiom,
! [V_y_2: $i,V_x_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_x_2 )
= ( hAPP @ c_Code__Numeral_Onat__of @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Onat__of__inject) ).
thf(1000,axiom,
! [V_m_2: $i,V_n_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Oof__nat @ V_n_2 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ V_m_2 ) )
<=> ( V_n_2 = V_m_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__inject) ).
thf(1220,axiom,
! [V_us: $i,V_ys: $i,V_zs: $i,V_xs1: $i,V_xs: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_xs1 )
= V_zs )
=> ( ( V_ys
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs1 ) @ V_us ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs ) @ V_us ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__appendI) ).
thf(1221,axiom,
! [V_zs_2: $i,V_xs_2: $i,V_ys_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_ys_2 ) @ V_xs_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_xs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__same__eq) ).
thf(1222,axiom,
! [V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_zs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__append__eq) ).
thf(1223,axiom,
! [V_tsa_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_tsa_2 ) )
<=> ? [B_us: $i] :
( ( ( V_xs_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ B_us ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ys_2 )
= V_tsa_2 ) )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ B_us )
= V_zs_2 )
& ( V_ys_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_tsa_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__append__conv2) ).
thf(1224,axiom,
! [V_zs: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys ) ) @ V_zs )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_ys ) @ V_zs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__assoc) ).
thf(1328,axiom,
! [V_y: $i,V_x: $i,V_i: $i,V_xs: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__overwrite) ).
thf(1329,axiom,
! [V_x_H: $i,V_x: $i,V_xs: $i,T_a: $i,V_i_H: $i,V_i: $i] :
( ( V_i != V_i_H )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i_H ) @ V_x_H )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i_H ) @ V_x_H ) ) @ V_i ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__swap) ).
thf(1445,axiom,
! [V_x: $i,T_a: $i,V_xs: $i] :
( V_xs
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self) ).
thf(1446,axiom,
! [V_xs: $i,V_x: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs )
!= V_xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self2) ).
thf(1447,axiom,
! [V_list_H_2: $i,V_a_H_2: $i,V_list_2: $i,V_a_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_2 ) @ V_list_2 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_H_2 ) @ V_list_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_list_2 = V_list_H_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Oinject) ).
thf(1502,axiom,
! [V_x_2: $i,V_n_2: $i,T_b: $i,V_f_2: $i] :
( ( hAPP @ V_f_2 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_n_2 ) @ V_f_2 ) @ V_x_2 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_n_2 ) @ V_f_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__swap1) ).
thf(1543,axiom,
! [V_r_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_c @ T_b ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_c ) @ V_r_2 ) )
= V_r_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__converse) ).
thf(1675,axiom,
! [T_b: $i,V_x_2: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_someI) ).
thf(1676,axiom,
! [T_b: $i,B_P: $i] :
( ? [B_x: $i] : ( hBOOL @ ( hAPP @ B_P @ B_x ) )
=> ( hBOOL @ ( hAPP @ B_P @ ( c_Hilbert__Choice_OEps @ T_b @ B_P ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tfl__some) ).
thf(1677,axiom,
! [T_b: $i,V_P_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_someI__ex) ).
thf(1678,axiom,
! [T_b: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) ) )
<=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_some__eq__ex) ).
thf(1681,axiom,
! [T_b: $i,V_c_2: $i,V_P_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
=> ( ( V_c_2
= ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ V_c_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_exE__some) ).
thf(1709,axiom,
! [V_p_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Wellfounded_OwfP @ T_b @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_p_2 ) @ V_r_2 ) )
=> ( c_Wellfounded_OwfP @ T_b @ V_p_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__subset) ).
thf(1722,axiom,
! [V_a1_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_b @ T_c @ V_r_2 ) @ V_a1_2 ) )
<=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_x1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP_Oequations) ).
thf(1723,axiom,
! [T_c: $i,T_b: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_b @ T_c @ V_r_2 ) @ V_a_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).
thf(1778,axiom,
! [V_a2_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_b @ T_c @ V_r_2 ) @ V_a2_2 ) )
<=> ? [B_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_a ) @ V_a2_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).
thf(1779,axiom,
! [V_a3_2: $i,V_a1_2: $i,V_s_2: $i,V_r_2: $i,T_d: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ T_b @ T_c @ T_d @ V_r_2 @ V_s_2 ) @ V_a1_2 ) @ V_a3_2 ) )
<=> ? [B_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_b ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ B_b ) @ V_a3_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__comp_Oequations) ).
thf(1780,axiom,
! [T_c: $i,T_b: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_b @ T_c @ V_r_2 ) @ V_b_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).
thf(1781,axiom,
! [T_d: $i,T_c: $i,T_b: $i,V_c_2: $i,V_s_2: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ V_b_2 ) @ V_c_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ T_b @ T_c @ T_d @ V_r_2 @ V_s_2 ) @ V_a_2 ) @ V_c_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__comp_Ointros) ).
thf(1802,axiom,
! [V_T_2: $i,V_S_2: $i,V_R_2: $i,T_e: $i,T_c: $i,T_d: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_d @ T_c ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_d ) @ V_R_2 ) @ V_S_2 ) ) @ V_T_2 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_c ) @ V_R_2 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_e @ T_d @ T_c ) @ V_S_2 ) @ V_T_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_O__assoc) ).
thf(1826,axiom,
! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__apply) ).
thf(1827,axiom,
! [V_x_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Predicate_Oreflp @ T_b @ V_r_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflpE) ).
thf(1829,axiom,
! [V_x_1: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x_1 )
= V_x_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__def) ).
thf(1902,axiom,
! [V_P_2: $i,T_b: $i] :
( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 )
= V_P_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
thf(2005,axiom,
! [V_f_2: $i,T_c: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) ) @ ( hAPP @ ( c_Set_Ovimage @ T_c @ T_b @ V_f_2 ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__mono) ).
thf(2007,axiom,
! [V_x_2: $i,V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ T_b @ T_c @ V_f_2 ) @ V_A_2 ) @ V_x_2 ) )
<=> ( hBOOL @ ( hAPP @ V_A_2 @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__code) ).
thf(2034,axiom,
! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
( ( c_Typedef_Otype__definition @ T_b @ T_c @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( ( hAPP @ V_Rep_2 @ V_x_2 )
= ( hAPP @ V_Rep_2 @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).
thf(2035,axiom,
! [V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
( ( c_Typedef_Otype__definition @ T_b @ T_c @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( hAPP @ V_Abs_2 @ ( hAPP @ V_Rep_2 @ V_x_2 ) )
= V_x_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).
thf(2057,axiom,
! [V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
<=> ! [B_x: $i,B_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_y ) )
<=> ( ( hAPP @ V_R_2 @ B_x )
= ( hAPP @ V_R_2 @ B_y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__def) ).
thf(2058,axiom,
! [V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__reflp) ).
thf(2059,axiom,
! [V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__symp) ).
thf(2060,axiom,
! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_z_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__transp) ).
thf(2216,axiom,
! [V_y_2: $i,V_x_2: $i] :
( ( ( hAPP @ c_Int_ORep__Integ @ V_x_2 )
= ( hAPP @ c_Int_ORep__Integ @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
thf(2270,axiom,
! [V_a_2: $i,V_r_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_a_2 ) )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ B_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp_Osimps) ).
thf(2271,axiom,
! [V_a_2: $i,V_r_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_a_2 ) )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ B_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp_Oequations) ).
thf(2272,axiom,
! [V_a_2: $i,V_b_2: $i,V_r_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_b_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_a_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__downward) ).
thf(2280,axiom,
! [V_R2_2: $i,V_R1_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_R1_2 ) @ V_R2_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ T_b @ V_R2_2 ) ) @ ( c_Wellfounded_Oaccp @ T_b @ V_R1_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__subset) ).
thf(2294,axiom,
! [V_qr_H: $i,V_qr: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr_H ) )
=> ( V_qr = V_qr_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__unique) ).
thf(2315,axiom,
! [V_c_2: $i,T_d: $i,T_c: $i,T_b: $i,V_q_2: $i,V_p_2: $i] :
( ( V_p_2 = V_q_2 )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_p_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_q_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__weak__cong) ).
thf(2316,axiom,
! [V_b_H: $i,V_a_H: $i,V_b: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_H ) @ V_b_H ) )
=> ~ ( ( V_a = V_a_H )
=> ( V_b != V_b_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(2317,axiom,
! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_c: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_H_2 ) @ V_b_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_b_2 = V_b_H_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(2318,axiom,
! [T_c: $i,T_b: $i,V_P_2: $i] :
( ! [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
<=> ! [B_a: $i,B_b: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ B_a ) @ B_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__All) ).
thf(2354,axiom,
! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2D2) ).
thf(2355,axiom,
! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2D1) ).
thf(2356,axiom,
! [V_B_2: $i,T_c: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2I1) ).
thf(2357,axiom,
! [V_A_2: $i,T_c: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_B_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2I2) ).
thf(2359,axiom,
! [V_Q_2: $i,T_c: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_P_2 ) @ V_Q_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_2 @ V_x_2 ) @ V_y_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
thf(2360,axiom,
! [V_y_2: $i,V_x_2: $i,V_Q_2: $i,V_P_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_P_2 ) @ V_Q_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_2 @ V_x_2 ) @ V_y_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate2D) ).
thf(2364,axiom,
! [V_y_2: $i,V_x_2: $i,T_c: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_x_2 ) @ V_y_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot2E) ).
thf(2365,axiom,
! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2E) ).
thf(2366,axiom,
! [T_c: $i,T_b: $i,V_B_2: $i,V_y_2: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2I) ).
thf(2367,axiom,
! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2E) ).
thf(2368,axiom,
! [T_c: $i,T_b: $i,V_A_2: $i,V_y_2: $i,V_x_2: $i,V_B_2: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2CI) ).
thf(2555,axiom,
! [V_b_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_a_2: $i,V_x_2: $i] :
( ( ( V_x_2 = V_a_2 )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_a_2 @ V_b_2 ) @ V_x_2 )
= V_b_2 ) )
& ( ( V_x_2 != V_a_2 )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_a_2 @ V_b_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__def) ).
thf(2556,axiom,
! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__def) ).
thf(2557,axiom,
! [V_h_2: $i,V_g_2: $i,T_e: $i,V_f_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_f_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_d @ T_b @ V_g_2 ) @ V_h_2 ) )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_e @ V_f_2 ) @ V_g_2 ) ) @ V_h_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__assoc) ).
thf(2558,axiom,
! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__apply) ).
thf(2559,axiom,
! [V_v_2: $i,V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest) ).
thf(2560,axiom,
! [V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
=> ! [B_v: $i] :
( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__elim) ).
thf(2576,axiom,
! [V_v_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= V_c_2 )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ V_v_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).
thf(2577,axiom,
! [T_f: $i,T_e: $i,T_d: $i,T_b: $i,T_c: $i,V_x_H_2: $i,V_g_H_2: $i,V_f_H_2: $i,V_x_2: $i,V_g_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) )
= ( hAPP @ V_f_H_2 @ ( hAPP @ V_g_H_2 @ V_x_H_2 ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_b @ T_f @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__cong) ).
thf(3452,axiom,
! [V_w: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_z ) @ V_w ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_w ) @ V_z ) )
=> ( V_z = V_w ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__antisym) ).
thf(3453,axiom,
! [V_k: $i,V_j: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_i ) @ V_j ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_j ) @ V_k ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_i ) @ V_k ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__trans) ).
thf(3454,axiom,
! [V_w: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_z ) @ V_w ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_w ) @ V_z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__linear) ).
thf(3455,axiom,
! [V_w: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_w ) @ V_w ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__refl) ).
thf(3512,axiom,
! [V_x_2: $i,V_F_2: $i,V_g_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ T_b @ T_c @ V_f_2 @ V_z_2 @ V_g_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
thf(3603,axiom,
! [V_z_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ T_b @ T_c @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__idem) ).
thf(4064,axiom,
! [V_y: $i,V_x: $i] :
( ( ( hAPP @ c_Nat_OSuc @ V_x )
= ( hAPP @ c_Nat_OSuc @ V_y ) )
=> ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(4065,axiom,
! [V_nat_H_2: $i,V_nat_2: $i] :
( ( ( hAPP @ c_Nat_OSuc @ V_nat_2 )
= ( hAPP @ c_Nat_OSuc @ V_nat_H_2 ) )
<=> ( V_nat_2 = V_nat_H_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(4066,axiom,
! [V_n: $i] :
( ( hAPP @ c_Nat_OSuc @ V_n )
!= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(4067,axiom,
! [V_n: $i] :
( V_n
!= ( hAPP @ c_Nat_OSuc @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(4114,axiom,
! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofun__left__comm @ T_b @ T_c @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm) ).
thf(4230,axiom,
! [V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_m ) @ V_n ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_n ) @ V_m ) )
=> ( V_m = V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(4231,axiom,
! [V_k: $i,V_j: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_i ) @ V_j ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_j ) @ V_k ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_i ) @ V_k ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
thf(4237,axiom,
! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_m ) @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(4239,axiom,
! [V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_m ) @ V_n ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_n ) @ V_m ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(4245,axiom,
! [V_n: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_n ) @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
thf(4399,axiom,
! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ T_b @ V_f_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
thf(4415,axiom,
! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ V_y_2 )
= V_f_2 )
<=> ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).
thf(4417,axiom,
! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ T_c @ T_b @ V_f_2 @ V_x_2 @ V_y_2 ) @ V_x_2 )
= V_y_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__same) ).
thf(4418,axiom,
! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
( ( ( V_z_2 = V_x_2 )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ V_y_2 ) @ V_z_2 )
= V_y_2 ) )
& ( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__apply) ).
thf(4420,axiom,
! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__other) ).
thf(4421,axiom,
! [T_b: $i,T_c: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 )
=> ( ( c_Fun_Ofun__upd @ T_c @ T_b @ V_f_2 @ V_x_2 @ V_y_2 )
= V_f_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem) ).
thf(4422,axiom,
! [V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ ( hAPP @ V_f_2 @ V_x_2 ) )
= V_f_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__triv) ).
thf(4568,axiom,
! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__mp) ).
thf(4569,axiom,
! [V_B_2: $i,V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev__mp) ).
thf(4570,axiom,
! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mono) ).
thf(4581,axiom,
! [V_A_2: $i,T_b: $i,V_b_2: $i,V_a_2: $i] :
( ( V_a_2 = V_b_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_b_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem__trans) ).
thf(4582,axiom,
! [V_A_2: $i,T_b: $i,V_y_2: $i,V_x_2: $i] :
( ( V_x_2 = V_y_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_y_2 ) @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).
thf(4583,axiom,
! [V_x_2: $i,T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).
thf(4585,axiom,
! [V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
thf(4599,axiom,
! [V_c_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subsetD) ).
thf(4603,axiom,
! [V_c_2: $i,T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_A_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_B_2 ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_B_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityCE) ).
thf(4628,axiom,
! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
thf(4629,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset) ).
thf(4684,axiom,
! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_A_2 ) )
= V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__diff) ).
thf(4685,axiom,
! [V_B_2: $i,V_D_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_D_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__mono) ).
thf(4686,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__subset) ).
thf(4696,axiom,
! [V_A_2: $i,V_B_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_B_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__inj__on) ).
thf(4704,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_B_2 )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__idemp) ).
thf(4787,axiom,
! [V_f_2: $i,T_c: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ T_b @ T_c @ V_f_2 ) @ V_A_2 ) ) @ ( hAPP @ ( c_Set_Oimage @ T_b @ T_c @ V_f_2 ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__mono) ).
thf(4788,axiom,
! [V_A_2: $i,V_f_2: $i,T_c: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) ) )
<=> ? [B_AA: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) @ B_AA ) @ V_A_2 ) )
& ( V_B_2
= ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ B_AA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__image__iff) ).
thf(4821,axiom,
! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__trans) ).
thf(4863,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
& ( V_A_2 != V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__eq) ).
thf(4864,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
| ( V_A_2 = V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
thf(4865,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
thf(4866,axiom,
! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
thf(4867,axiom,
! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
thf(4879,axiom,
! [V_a_2: $i,V_B_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI) ).
thf(4880,axiom,
! [V_b_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2) ).
thf(4881,axiom,
! [V_a_2: $i,V_D_2: $i,V_C_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_C_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_D_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__mono) ).
thf(4914,axiom,
! [V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb2) ).
thf(4915,axiom,
! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__commute) ).
thf(4916,axiom,
! [V_x_2: $i,V_A_2: $i,V_y_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ V_A_2 ) @ V_x_2 ) )
<=> ( ( V_y_2 = V_x_2 )
| ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
thf(4986,axiom,
! [V_D_2: $i,V_B_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_D_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__mono) ).
thf(4987,axiom,
! [V_B_2: $i,V_A_2: $i,V_C_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_A_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__greatest) ).
thf(4988,axiom,
! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb1) ).
thf(4989,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb2) ).
thf(4990,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower2) ).
thf(4991,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower1) ).
thf(4994,axiom,
! [V_D_2: $i,V_B_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_D_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__mono) ).
thf(4995,axiom,
! [V_B_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__least) ).
thf(4996,axiom,
! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb2) ).
thf(4997,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb1) ).
thf(4998,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Un__eq) ).
thf(4999,axiom,
! [V_A_2: $i,V_B_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper2) ).
thf(5000,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper1) ).
thf(5092,axiom,
! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D2) ).
thf(5093,axiom,
! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D1) ).
thf(5094,axiom,
! [V_A_2: $i,T_b: $i,V_x_2: $i,V_B_2: $i] :
( ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I2) ).
thf(5095,axiom,
! [V_B_2: $i,T_b: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I1) ).
thf(5101,axiom,
! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__assoc) ).
thf(5102,axiom,
! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__assoc) ).
thf(5105,axiom,
! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__commute) ).
thf(5106,axiom,
! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__commute) ).
thf(5107,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__absorb) ).
thf(5108,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__absorb) ).
thf(5109,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__commute) ).
thf(5110,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__commute) ).
thf(5111,axiom,
! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
= V_A_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb) ).
thf(5112,axiom,
! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
= V_A_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb) ).
thf(5116,axiom,
! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ~ ( ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ~ ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1E) ).
thf(5117,axiom,
! [T_b: $i,V_B_2: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ( ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1I) ).
thf(5118,axiom,
! [T_b: $i,V_A_2: $i,V_x_2: $i,V_B_2: $i] :
( ( ~ ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1CI) ).
thf(5119,axiom,
! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ( ~ ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1E) ).
thf(5135,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_A_2 ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__mono) ).
thf(5142,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__subset__Compl__iff) ).
thf(5143,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__anti__mono) ).
thf(5148,axiom,
! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) )
= V_A_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
thf(5149,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) )
<=> ( V_A_2 = V_B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__eq__Compl__iff) ).
thf(5155,axiom,
! [V_x_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_x_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top1I) ).
thf(5162,axiom,
! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_A_2 ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__anti__mono) ).
thf(5165,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ T_b ) @ V_A_2 ) ) @ ( hAPP @ ( c_Set_OPow @ T_b ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__mono) ).
thf(5168,axiom,
! [V_a_2: $i,T_b: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_a_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_Oequations_I1_J) ).
thf(5169,axiom,
! [V_G_2: $i,T_b: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty) ).
thf(5170,axiom,
! [V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__empty) ).
thf(5171,axiom,
! [V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV) ).
thf(5180,axiom,
! [V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__subsetI) ).
thf(5190,axiom,
! [T_b: $i,V_g_2: $i,V_f_2: $i,T_c: $i] :
( ( class_Orderings_Oord @ T_c )
=> ( ! [B_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_c ) @ ( hAPP @ V_f_2 @ B_x ) ) @ ( hAPP @ V_g_2 @ B_x ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ T_c ) ) @ V_f_2 ) @ V_g_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funI) ).
thf(5191,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ T_b @ V_A_2 ) ) @ ( c_Predicate_OPowp @ T_b @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Powp__mono) ).
thf(5192,axiom,
! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityE) ).
thf(5193,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
thf(5194,axiom,
! [V_y_2: $i,V_x_2: $i,T_b: $i] :
( ( class_Orderings_Oorder @ T_b )
=> ( ( V_x_2 = V_y_2 )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_x_2 ) @ V_y_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_y_2 ) @ V_x_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
thf(5195,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( V_x = V_y )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl) ).
thf(5196,axiom,
! [V_x_2: $i,V_y_2: $i,T_b: $i] :
( ( class_Orderings_Oorder @ T_b )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_y_2 ) @ V_x_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_x_2 ) @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
thf(5197,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oord @ T_a )
=> ( ( V_a = V_b )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_b ) @ V_c ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_a ) @ V_c ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).
thf(5198,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( V_a = V_b )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_c ) @ V_b ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_c ) @ V_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I3_J) ).
thf(5199,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oord @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_a ) @ V_b ) )
=> ( ( V_b = V_c )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_a ) @ V_c ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
thf(5200,axiom,
! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_b ) @ V_a ) )
=> ( ( V_b = V_c )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_c ) @ V_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I4_J) ).
thf(5201,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) )
=> ( V_x = V_y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
thf(5202,axiom,
! [V_z: $i,V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_z ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_z ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
thf(5203,axiom,
! [V_x: $i,V_y: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( V_x = V_y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
thf(5204,axiom,
! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_z ) @ V_y ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_z ) @ V_x ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
thf(5205,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
thf(5206,axiom,
! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).
thf(5207,axiom,
! [V_x_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_P_2 ) @ V_Q_2 ) )
=> ( ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_Q_2 @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).
thf(5208,axiom,
! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD2) ).
thf(5209,axiom,
! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD1) ).
thf(5210,axiom,
! [V_Q_2: $i,T_b: $i,V_x_2: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_P_2 ) @ V_Q_2 ) )
=> ( hBOOL @ ( hAPP @ V_Q_2 @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
thf(5211,axiom,
! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__eq__subset) ).
thf(5212,axiom,
! [V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).
thf(5213,axiom,
! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( class_Orderings_Oord @ T_c )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ T_c ) ) @ V_f_2 ) @ V_g_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_c ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
thf(5214,axiom,
! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( class_Orderings_Oord @ T_c )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ T_c ) ) @ V_f_2 ) @ V_g_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_c ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
thf(5215,axiom,
! [V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( class_Orderings_Oord @ T_c )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ T_c ) ) @ V_f_2 ) @ V_g_2 ) )
<=> ! [B_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_c ) @ ( hAPP @ V_f_2 @ B_x ) ) @ ( hAPP @ V_g_2 @ B_x ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
thf(5216,axiom,
! [V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
thf(5217,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( V_A_2 = V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityI) ).
thf(5218,axiom,
! [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_Ha_2 @ V_tsa_2 )
=> ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_G_Ha_2 )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_tsa_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cut) ).
thf(5219,axiom,
! [V_tsa_2: $i,V_ts_H_2: $i,V_G_2: $i,T_b: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_ts_H_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) @ V_tsa_2 ) @ V_ts_H_2 ) )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_tsa_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_weaken) ).
thf(5220,axiom,
! [V_G_2: $i,V_tsa_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) @ V_tsa_2 ) @ V_G_2 ) )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_tsa_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_asm) ).
thf(5221,axiom,
! [V_g_2: $i,V_f_2: $i] :
( ! [B_x: $i] :
( ( hAPP @ V_f_2 @ B_x )
= ( hAPP @ V_g_2 @ B_x ) )
=> ( V_f_2 = V_g_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
thf(5222,axiom,
c_Hoare__Mirabelle_Ohoare__derivs @ t_a @ v_G_H @ v_ts,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(5223,conjecture,
! [B_G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_HOL_Obool ) ) @ v_G_H ) @ B_G ) )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ t_a @ B_G @ v_ts ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(5224,negated_conjecture,
( ( ! [B_G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_HOL_Obool ) ) @ v_G_H ) @ B_G ) )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ t_a @ B_G @ v_ts ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5223]) ).
thf(5225,plain,
( ( ! [B_G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_HOL_Obool ) ) @ v_G_H ) @ B_G ) )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ t_a @ B_G @ v_ts ) ) )
= $false ),
inference(unfold_def,[status(thm)],[5224]) ).
thf(5226,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) )
| ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(5227,plain,
( ( ! [V_P_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(5228,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(5229,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_P_2 )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(5230,plain,
( ( ! [V_P_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(5231,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(5232,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(5233,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_P_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(5234,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ V_P_2 )
| ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(5235,plain,
( ( ! [V_P_2: $i] :
( ~ ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(5236,plain,
( ( ! [V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) )
| ~ ( hBOOL @ V_P_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(5237,plain,
( ( hBOOL @ c_fTrue )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(5238,plain,
( ( ~ ( hBOOL @ c_fFalse ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(5239,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(5240,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) )
| ( V_x_2 = V_y_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(5241,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_c @ T_d @ T_b ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(5242,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_c @ T_d @ T_b ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ V_Q_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(5243,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_c @ T_b @ T_d ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ V_P_2 @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(5244,plain,
( ( ! [V_Q: $i,V_P: $i,T_b: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ T_a @ T_b ) @ V_P ) @ V_Q )
= V_P ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(5245,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
= V_P ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(5246,plain,
( ( ! [T_1: $i] : ( class_Nat_Osize @ ( tc_Hoare__Mirabelle_Otriple @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(5247,plain,
( ( class_Nat_Osize @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(5248,plain,
( ( class_Enum_Oenum @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(5249,plain,
( ( class_Groups_Ominus @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(5250,plain,
( ( class_Groups_Ouminus @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(5251,plain,
( ( class_Orderings_Obot @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(5252,plain,
( ( class_Orderings_Oord @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(5253,plain,
( ( class_Orderings_Otop @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(5254,plain,
( ( class_Orderings_Oorder @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(5255,plain,
( ( class_Lattices_Olattice @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(5256,plain,
( ( class_Finite__Set_Ofinite @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(5257,plain,
( ( class_Orderings_Opreorder @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(5258,plain,
( ( class_Lattices_Oboolean__algebra @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(5259,plain,
( ( class_Lattices_Odistrib__lattice @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(5260,plain,
( ( class_Lattices_Osemilattice__inf @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(5261,plain,
( ( class_Lattices_Osemilattice__sup @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(5262,plain,
( ( class_Lattices_Obounded__lattice__bot @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(5263,plain,
( ( class_Lattices_Obounded__lattice__top @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(5264,plain,
( ( class_Complete__Lattice_Ocomplete__lattice @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(5265,plain,
( ( ! [T_1: $i,T_2: $i] :
( ( ( class_Enum_Oenum @ T_2 )
& ( class_Enum_Oenum @ T_1 ) )
=> ( class_Enum_Oenum @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(5266,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Groups_Ominus @ T_1 )
=> ( class_Groups_Ominus @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(5267,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Groups_Ouminus @ T_1 )
=> ( class_Groups_Ouminus @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(5268,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Obot @ T_1 )
=> ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(5269,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oord @ T_1 )
=> ( class_Orderings_Oord @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(5270,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Otop @ T_1 )
=> ( class_Orderings_Otop @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(5271,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ T_1 )
=> ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(5272,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olattice @ T_1 )
=> ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(5273,plain,
( ( ! [T_1: $i,T_2: $i] :
( ( ( class_Finite__Set_Ofinite @ T_2 )
& ( class_Finite__Set_Ofinite @ T_1 ) )
=> ( class_Finite__Set_Ofinite @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(5274,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ T_1 )
=> ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(5275,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Oboolean__algebra @ T_1 )
=> ( class_Lattices_Oboolean__algebra @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(5276,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Odistrib__lattice @ T_1 )
=> ( class_Lattices_Odistrib__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(5277,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ T_1 )
=> ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(5278,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Obounded__lattice @ T_1 )
=> ( class_Lattices_Obounded__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(5279,plain,
( ( class_Lattices_Obounded__lattice @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(5280,plain,
( ( ! [V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ T_b @ V_R_2 ) @ V_x_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(5281,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Opart__equivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_z_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(5282,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Opart__equivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(5283,plain,
( ( ! [V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Opart__equivp @ T_b @ V_R_2 )
<=> ( ? [B_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_x ) )
& ! [B_x: $i,B_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_y ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_x ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_y ) @ B_y ) )
& ( ( hAPP @ V_R_2 @ B_x )
= ( hAPP @ V_R_2 @ B_y ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(5284,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Predicate_Osymp @ T_b @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_y_2 ) @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(5285,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Predicate_Otransp @ T_b @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_y_2 ) @ V_z_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(5286,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_b_2 ) @ V_a_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[559]) ).
thf(5287,plain,
( ( ! [T_c: $i,T_b: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_b_2 ) @ V_a_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[560]) ).
thf(5288,plain,
( ( ! [V_a1_2: $i,V_a2_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_a2_2 ) @ V_a1_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ V_a2_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[561]) ).
thf(5289,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_a_2 ) @ V_b_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_b_2 ) @ V_a_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[562]) ).
thf(5290,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( hAPP @ ( c_List_Orev @ T_a ) @ ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs ) )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[720]) ).
thf(5291,plain,
( ( ! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
= V_ys_2 )
<=> ( V_xs_2
= ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[721]) ).
thf(5292,plain,
( ( ! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
= ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) )
<=> ( V_xs_2 = V_ys_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[722]) ).
thf(5293,plain,
( ( ! [V_l_2: $i,V_k_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_k_2 )
= ( hAPP @ c_Code__Numeral_Onat__of @ V_l_2 ) )
<=> ( V_k_2 = V_l_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[972]) ).
thf(5294,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_x_2 )
= ( hAPP @ c_Code__Numeral_Onat__of @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[973]) ).
thf(5295,plain,
( ( ! [V_m_2: $i,V_n_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Oof__nat @ V_n_2 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ V_m_2 ) )
<=> ( V_n_2 = V_m_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1000]) ).
thf(5296,plain,
( ( ! [V_us: $i,V_ys: $i,V_zs: $i,V_xs1: $i,V_xs: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_xs1 )
= V_zs )
=> ( ( V_ys
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs1 ) @ V_us ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs ) @ V_us ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1220]) ).
thf(5297,plain,
( ( ! [V_zs_2: $i,V_xs_2: $i,V_ys_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_ys_2 ) @ V_xs_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_xs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1221]) ).
thf(5298,plain,
( ( ! [V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_zs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1222]) ).
thf(5299,plain,
( ( ! [V_tsa_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_tsa_2 ) )
<=> ? [B_us: $i] :
( ( ( V_xs_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ B_us ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ys_2 )
= V_tsa_2 ) )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ B_us )
= V_zs_2 )
& ( V_ys_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_tsa_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1223]) ).
thf(5300,plain,
( ( ! [V_zs: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys ) ) @ V_zs )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_ys ) @ V_zs ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1224]) ).
thf(5301,plain,
( ( ! [V_y: $i,V_x: $i,V_i: $i,V_xs: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1328]) ).
thf(5302,plain,
( ( ! [V_x_H: $i,V_x: $i,V_xs: $i,T_a: $i,V_i_H: $i,V_i: $i] :
( ( V_i != V_i_H )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i_H ) @ V_x_H )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i_H ) @ V_x_H ) ) @ V_i ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1329]) ).
thf(5303,plain,
( ( ! [V_x: $i,T_a: $i,V_xs: $i] :
( V_xs
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1445]) ).
thf(5304,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs )
!= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[1446]) ).
thf(5305,plain,
( ( ! [V_list_H_2: $i,V_a_H_2: $i,V_list_2: $i,V_a_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_2 ) @ V_list_2 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_H_2 ) @ V_list_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_list_2 = V_list_H_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1447]) ).
thf(5306,plain,
( ( ! [V_x_2: $i,V_n_2: $i,T_b: $i,V_f_2: $i] :
( ( hAPP @ V_f_2 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_n_2 ) @ V_f_2 ) @ V_x_2 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_n_2 ) @ V_f_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1502]) ).
thf(5307,plain,
( ( ! [V_r_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_c @ T_b ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_c ) @ V_r_2 ) )
= V_r_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[1543]) ).
thf(5308,plain,
( ( ! [T_b: $i,V_x_2: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1675]) ).
thf(5309,plain,
( ( ! [T_b: $i,B_P: $i] :
( ? [B_x: $i] : ( hBOOL @ ( hAPP @ B_P @ B_x ) )
=> ( hBOOL @ ( hAPP @ B_P @ ( c_Hilbert__Choice_OEps @ T_b @ B_P ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1676]) ).
thf(5310,plain,
( ( ! [T_b: $i,V_P_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1677]) ).
thf(5311,plain,
( ( ! [T_b: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) ) )
<=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1678]) ).
thf(5312,plain,
( ( ! [T_b: $i,V_c_2: $i,V_P_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
=> ( ( V_c_2
= ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ V_c_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1681]) ).
thf(5313,plain,
( ( ! [V_p_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Wellfounded_OwfP @ T_b @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_p_2 ) @ V_r_2 ) )
=> ( c_Wellfounded_OwfP @ T_b @ V_p_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1709]) ).
thf(5314,plain,
( ( ! [V_a1_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_b @ T_c @ V_r_2 ) @ V_a1_2 ) )
<=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_x1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1722]) ).
thf(5315,plain,
( ( ! [T_c: $i,T_b: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_b @ T_c @ V_r_2 ) @ V_a_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1723]) ).
thf(5316,plain,
( ( ! [V_a2_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_b @ T_c @ V_r_2 ) @ V_a2_2 ) )
<=> ? [B_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_a ) @ V_a2_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1778]) ).
thf(5317,plain,
( ( ! [V_a3_2: $i,V_a1_2: $i,V_s_2: $i,V_r_2: $i,T_d: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ T_b @ T_c @ T_d @ V_r_2 @ V_s_2 ) @ V_a1_2 ) @ V_a3_2 ) )
<=> ? [B_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_b ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ B_b ) @ V_a3_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1779]) ).
thf(5318,plain,
( ( ! [T_c: $i,T_b: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_b @ T_c @ V_r_2 ) @ V_b_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1780]) ).
thf(5319,plain,
( ( ! [T_d: $i,T_c: $i,T_b: $i,V_c_2: $i,V_s_2: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ V_b_2 ) @ V_c_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ T_b @ T_c @ T_d @ V_r_2 @ V_s_2 ) @ V_a_2 ) @ V_c_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1781]) ).
thf(5320,plain,
( ( ! [V_T_2: $i,V_S_2: $i,V_R_2: $i,T_e: $i,T_c: $i,T_d: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_d @ T_c ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_d ) @ V_R_2 ) @ V_S_2 ) ) @ V_T_2 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_c ) @ V_R_2 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_e @ T_d @ T_c ) @ V_S_2 ) @ V_T_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1802]) ).
thf(5321,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[1826]) ).
thf(5322,plain,
( ( ! [V_x_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Predicate_Oreflp @ T_b @ V_r_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1827]) ).
thf(5323,plain,
( ( ! [V_x_1: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x_1 )
= V_x_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[1829]) ).
thf(5324,plain,
( ( ! [V_P_2: $i,T_b: $i] :
( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 )
= V_P_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[1902]) ).
thf(5325,plain,
( ( ! [V_f_2: $i,T_c: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) ) @ ( hAPP @ ( c_Set_Ovimage @ T_c @ T_b @ V_f_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2005]) ).
thf(5326,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ T_b @ T_c @ V_f_2 ) @ V_A_2 ) @ V_x_2 ) )
<=> ( hBOOL @ ( hAPP @ V_A_2 @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2007]) ).
thf(5327,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
( ( c_Typedef_Otype__definition @ T_b @ T_c @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( ( hAPP @ V_Rep_2 @ V_x_2 )
= ( hAPP @ V_Rep_2 @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2034]) ).
thf(5328,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
( ( c_Typedef_Otype__definition @ T_b @ T_c @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( hAPP @ V_Abs_2 @ ( hAPP @ V_Rep_2 @ V_x_2 ) )
= V_x_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2035]) ).
thf(5329,plain,
( ( ! [V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
<=> ! [B_x: $i,B_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_y ) )
<=> ( ( hAPP @ V_R_2 @ B_x )
= ( hAPP @ V_R_2 @ B_y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2057]) ).
thf(5330,plain,
( ( ! [V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2058]) ).
thf(5331,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2059]) ).
thf(5332,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_z_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2060]) ).
thf(5333,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ( ( hAPP @ c_Int_ORep__Integ @ V_x_2 )
= ( hAPP @ c_Int_ORep__Integ @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2216]) ).
thf(5334,plain,
( ( ! [V_a_2: $i,V_r_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_a_2 ) )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ B_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2270]) ).
thf(5335,plain,
( ( ! [V_a_2: $i,V_r_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_a_2 ) )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ B_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2271]) ).
thf(5336,plain,
( ( ! [V_a_2: $i,V_b_2: $i,V_r_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_b_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_a_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2272]) ).
thf(5337,plain,
( ( ! [V_R2_2: $i,V_R1_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_R1_2 ) @ V_R2_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ T_b @ V_R2_2 ) ) @ ( c_Wellfounded_Oaccp @ T_b @ V_R1_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2280]) ).
thf(5338,plain,
( ( ! [V_qr_H: $i,V_qr: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr_H ) )
=> ( V_qr = V_qr_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2294]) ).
thf(5339,plain,
( ( ! [V_c_2: $i,T_d: $i,T_c: $i,T_b: $i,V_q_2: $i,V_p_2: $i] :
( ( V_p_2 = V_q_2 )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_p_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2315]) ).
thf(5340,plain,
( ( ! [V_b_H: $i,V_a_H: $i,V_b: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_H ) @ V_b_H ) )
=> ~ ( ( V_a = V_a_H )
=> ( V_b != V_b_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2316]) ).
thf(5341,plain,
( ( ! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_c: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_H_2 ) @ V_b_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_b_2 = V_b_H_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2317]) ).
thf(5342,plain,
( ( ! [T_c: $i,T_b: $i,V_P_2: $i] :
( ! [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
<=> ! [B_a: $i,B_b: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ B_a ) @ B_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2318]) ).
thf(5343,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2354]) ).
thf(5344,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2355]) ).
thf(5345,plain,
( ( ! [V_B_2: $i,T_c: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2356]) ).
thf(5346,plain,
( ( ! [V_A_2: $i,T_c: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_B_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2357]) ).
thf(5347,plain,
( ( ! [V_Q_2: $i,T_c: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_P_2 ) @ V_Q_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_2 @ V_x_2 ) @ V_y_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2359]) ).
thf(5348,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_Q_2: $i,V_P_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_P_2 ) @ V_Q_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_2 @ V_x_2 ) @ V_y_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2360]) ).
thf(5349,plain,
( ( ! [V_y_2: $i,V_x_2: $i,T_c: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_x_2 ) @ V_y_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2364]) ).
thf(5350,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2365]) ).
thf(5351,plain,
( ( ! [T_c: $i,T_b: $i,V_B_2: $i,V_y_2: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2366]) ).
thf(5352,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2367]) ).
thf(5353,plain,
( ( ! [T_c: $i,T_b: $i,V_A_2: $i,V_y_2: $i,V_x_2: $i,V_B_2: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2368]) ).
thf(5354,plain,
( ( ! [V_b_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_a_2: $i,V_x_2: $i] :
( ( ( V_x_2 = V_a_2 )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_a_2 @ V_b_2 ) @ V_x_2 )
= V_b_2 ) )
& ( ( V_x_2 != V_a_2 )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_a_2 @ V_b_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2555]) ).
thf(5355,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2556]) ).
thf(5356,plain,
( ( ! [V_h_2: $i,V_g_2: $i,T_e: $i,V_f_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_f_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_d @ T_b @ V_g_2 ) @ V_h_2 ) )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_e @ V_f_2 ) @ V_g_2 ) ) @ V_h_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2557]) ).
thf(5357,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2558]) ).
thf(5358,plain,
( ( ! [V_v_2: $i,V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2559]) ).
thf(5359,plain,
( ( ! [V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
=> ! [B_v: $i] :
( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2560]) ).
thf(5360,plain,
( ( ! [V_v_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= V_c_2 )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ V_v_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2576]) ).
thf(5361,plain,
( ( ! [T_f: $i,T_e: $i,T_d: $i,T_b: $i,T_c: $i,V_x_H_2: $i,V_g_H_2: $i,V_f_H_2: $i,V_x_2: $i,V_g_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) )
= ( hAPP @ V_f_H_2 @ ( hAPP @ V_g_H_2 @ V_x_H_2 ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_b @ T_f @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2577]) ).
thf(5362,plain,
( ( ! [V_w: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_z ) @ V_w ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_w ) @ V_z ) )
=> ( V_z = V_w ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3452]) ).
thf(5363,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_i ) @ V_j ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_j ) @ V_k ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_i ) @ V_k ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3453]) ).
thf(5364,plain,
( ( ! [V_w: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_z ) @ V_w ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_w ) @ V_z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3454]) ).
thf(5365,plain,
( ( ! [V_w: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_w ) @ V_w ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3455]) ).
thf(5366,plain,
( ( ! [V_x_2: $i,V_F_2: $i,V_g_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ T_b @ T_c @ V_f_2 @ V_z_2 @ V_g_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3512]) ).
thf(5367,plain,
( ( ! [V_z_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ T_b @ T_c @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3603]) ).
thf(5368,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( ( hAPP @ c_Nat_OSuc @ V_x )
= ( hAPP @ c_Nat_OSuc @ V_y ) )
=> ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4064]) ).
thf(5369,plain,
( ( ! [V_nat_H_2: $i,V_nat_2: $i] :
( ( ( hAPP @ c_Nat_OSuc @ V_nat_2 )
= ( hAPP @ c_Nat_OSuc @ V_nat_H_2 ) )
<=> ( V_nat_2 = V_nat_H_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4065]) ).
thf(5370,plain,
( ( ! [V_n: $i] :
( ( hAPP @ c_Nat_OSuc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[4066]) ).
thf(5371,plain,
( ( ! [V_n: $i] :
( V_n
!= ( hAPP @ c_Nat_OSuc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4067]) ).
thf(5372,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofun__left__comm @ T_b @ T_c @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4114]) ).
thf(5373,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_m ) @ V_n ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_n ) @ V_m ) )
=> ( V_m = V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4230]) ).
thf(5374,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_i ) @ V_j ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_j ) @ V_k ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_i ) @ V_k ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4231]) ).
thf(5375,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_m ) @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4237]) ).
thf(5376,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_m ) @ V_n ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_n ) @ V_m ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4239]) ).
thf(5377,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_n ) @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4245]) ).
thf(5378,plain,
( ( ! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ T_b @ V_f_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4399]) ).
thf(5379,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ V_y_2 )
= V_f_2 )
<=> ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4415]) ).
thf(5380,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ T_c @ T_b @ V_f_2 @ V_x_2 @ V_y_2 ) @ V_x_2 )
= V_y_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[4417]) ).
thf(5381,plain,
( ( ! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
( ( ( V_z_2 = V_x_2 )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ V_y_2 ) @ V_z_2 )
= V_y_2 ) )
& ( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4418]) ).
thf(5382,plain,
( ( ! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4420]) ).
thf(5383,plain,
( ( ! [T_b: $i,T_c: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 )
=> ( ( c_Fun_Ofun__upd @ T_c @ T_b @ V_f_2 @ V_x_2 @ V_y_2 )
= V_f_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4421]) ).
thf(5384,plain,
( ( ! [V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ ( hAPP @ V_f_2 @ V_x_2 ) )
= V_f_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[4422]) ).
thf(5385,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4568]) ).
thf(5386,plain,
( ( ! [V_B_2: $i,V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4569]) ).
thf(5387,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4570]) ).
thf(5388,plain,
( ( ! [V_A_2: $i,T_b: $i,V_b_2: $i,V_a_2: $i] :
( ( V_a_2 = V_b_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_b_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4581]) ).
thf(5389,plain,
( ( ! [V_A_2: $i,T_b: $i,V_y_2: $i,V_x_2: $i] :
( ( V_x_2 = V_y_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_y_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4582]) ).
thf(5390,plain,
( ( ! [V_x_2: $i,T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4583]) ).
thf(5391,plain,
( ( ! [V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4585]) ).
thf(5392,plain,
( ( ! [V_c_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4599]) ).
thf(5393,plain,
( ( ! [V_c_2: $i,T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_A_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_B_2 ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_B_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4603]) ).
thf(5394,plain,
( ( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4628]) ).
thf(5395,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4629]) ).
thf(5396,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_A_2 ) )
= V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4684]) ).
thf(5397,plain,
( ( ! [V_B_2: $i,V_D_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_D_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4685]) ).
thf(5398,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4686]) ).
thf(5399,plain,
( ( ! [V_A_2: $i,V_B_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_B_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4696]) ).
thf(5400,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_B_2 )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4704]) ).
thf(5401,plain,
( ( ! [V_f_2: $i,T_c: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ T_b @ T_c @ V_f_2 ) @ V_A_2 ) ) @ ( hAPP @ ( c_Set_Oimage @ T_b @ T_c @ V_f_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4787]) ).
thf(5402,plain,
( ( ! [V_A_2: $i,V_f_2: $i,T_c: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) ) )
<=> ? [B_AA: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) @ B_AA ) @ V_A_2 ) )
& ( V_B_2
= ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ B_AA ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4788]) ).
thf(5403,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4821]) ).
thf(5404,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
& ( V_A_2 != V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4863]) ).
thf(5405,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
| ( V_A_2 = V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4864]) ).
thf(5406,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4865]) ).
thf(5407,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4866]) ).
thf(5408,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4867]) ).
thf(5409,plain,
( ( ! [V_a_2: $i,V_B_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4879]) ).
thf(5410,plain,
( ( ! [V_b_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4880]) ).
thf(5411,plain,
( ( ! [V_a_2: $i,V_D_2: $i,V_C_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_C_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_D_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4881]) ).
thf(5412,plain,
( ( ! [V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4914]) ).
thf(5413,plain,
( ( ! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4915]) ).
thf(5414,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_y_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ V_A_2 ) @ V_x_2 ) )
<=> ( ( V_y_2 = V_x_2 )
| ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4916]) ).
thf(5415,plain,
( ( ! [V_D_2: $i,V_B_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_D_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4986]) ).
thf(5416,plain,
( ( ! [V_B_2: $i,V_A_2: $i,V_C_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_A_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4987]) ).
thf(5417,plain,
( ( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4988]) ).
thf(5418,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4989]) ).
thf(5419,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4990]) ).
thf(5420,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4991]) ).
thf(5421,plain,
( ( ! [V_D_2: $i,V_B_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_D_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4994]) ).
thf(5422,plain,
( ( ! [V_B_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4995]) ).
thf(5423,plain,
( ( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4996]) ).
thf(5424,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4997]) ).
thf(5425,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4998]) ).
thf(5426,plain,
( ( ! [V_A_2: $i,V_B_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4999]) ).
thf(5427,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5000]) ).
thf(5428,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5092]) ).
thf(5429,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5093]) ).
thf(5430,plain,
( ( ! [V_A_2: $i,T_b: $i,V_x_2: $i,V_B_2: $i] :
( ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5094]) ).
thf(5431,plain,
( ( ! [V_B_2: $i,T_b: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5095]) ).
thf(5432,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5101]) ).
thf(5433,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5102]) ).
thf(5434,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5105]) ).
thf(5435,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5106]) ).
thf(5436,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5107]) ).
thf(5437,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5108]) ).
thf(5438,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5109]) ).
thf(5439,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5110]) ).
thf(5440,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
= V_A_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[5111]) ).
thf(5441,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
= V_A_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[5112]) ).
thf(5442,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ~ ( ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ~ ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5116]) ).
thf(5443,plain,
( ( ! [T_b: $i,V_B_2: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ( ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5117]) ).
thf(5444,plain,
( ( ! [T_b: $i,V_A_2: $i,V_x_2: $i,V_B_2: $i] :
( ( ~ ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5118]) ).
thf(5445,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ( ~ ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5119]) ).
thf(5446,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_A_2 ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5135]) ).
thf(5447,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5142]) ).
thf(5448,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5143]) ).
thf(5449,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) )
= V_A_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[5148]) ).
thf(5450,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) )
<=> ( V_A_2 = V_B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5149]) ).
thf(5451,plain,
( ( ! [V_x_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_x_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5155]) ).
thf(5452,plain,
( ( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_A_2 ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5162]) ).
thf(5453,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ T_b ) @ V_A_2 ) ) @ ( hAPP @ ( c_Set_OPow @ T_b ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5165]) ).
thf(5454,plain,
( ( ! [V_a_2: $i,T_b: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_a_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5168]) ).
thf(5455,plain,
( ( ! [V_G_2: $i,T_b: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5169]) ).
thf(5456,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5170]) ).
thf(5457,plain,
( ( ! [V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5171]) ).
thf(5458,plain,
( ( ! [V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5180]) ).
thf(5459,plain,
( ( ! [T_b: $i,V_g_2: $i,V_f_2: $i,T_c: $i] :
( ( class_Orderings_Oord @ T_c )
=> ( ! [B_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_c ) @ ( hAPP @ V_f_2 @ B_x ) ) @ ( hAPP @ V_g_2 @ B_x ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ T_c ) ) @ V_f_2 ) @ V_g_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5190]) ).
thf(5460,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ T_b @ V_A_2 ) ) @ ( c_Predicate_OPowp @ T_b @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5191]) ).
thf(5461,plain,
( ( ! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5192]) ).
thf(5462,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5193]) ).
thf(5463,plain,
( ( ! [V_y_2: $i,V_x_2: $i,T_b: $i] :
( ( class_Orderings_Oorder @ T_b )
=> ( ( V_x_2 = V_y_2 )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_x_2 ) @ V_y_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_y_2 ) @ V_x_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5194]) ).
thf(5464,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( V_x = V_y )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5195]) ).
thf(5465,plain,
( ( ! [V_x_2: $i,V_y_2: $i,T_b: $i] :
( ( class_Orderings_Oorder @ T_b )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_y_2 ) @ V_x_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_x_2 ) @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5196]) ).
thf(5466,plain,
( ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oord @ T_a )
=> ( ( V_a = V_b )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_b ) @ V_c ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_a ) @ V_c ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5197]) ).
thf(5467,plain,
( ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( V_a = V_b )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_c ) @ V_b ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_c ) @ V_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5198]) ).
thf(5468,plain,
( ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oord @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_a ) @ V_b ) )
=> ( ( V_b = V_c )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_a ) @ V_c ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5199]) ).
thf(5469,plain,
( ( ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_b ) @ V_a ) )
=> ( ( V_b = V_c )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_c ) @ V_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5200]) ).
thf(5470,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) )
=> ( V_x = V_y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5201]) ).
thf(5471,plain,
( ( ! [V_z: $i,V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_z ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_z ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5202]) ).
thf(5472,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( V_x = V_y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5203]) ).
thf(5473,plain,
( ( ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_z ) @ V_y ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_z ) @ V_x ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5204]) ).
thf(5474,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5205]) ).
thf(5475,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5206]) ).
thf(5476,plain,
( ( ! [V_x_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_P_2 ) @ V_Q_2 ) )
=> ( ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_Q_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5207]) ).
thf(5477,plain,
( ( ! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5208]) ).
thf(5478,plain,
( ( ! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5209]) ).
thf(5479,plain,
( ( ! [V_Q_2: $i,T_b: $i,V_x_2: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_P_2 ) @ V_Q_2 ) )
=> ( hBOOL @ ( hAPP @ V_Q_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5210]) ).
thf(5480,plain,
( ( ! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5211]) ).
thf(5481,plain,
( ( ! [V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5212]) ).
thf(5482,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( class_Orderings_Oord @ T_c )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ T_c ) ) @ V_f_2 ) @ V_g_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_c ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5213]) ).
thf(5483,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( class_Orderings_Oord @ T_c )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ T_c ) ) @ V_f_2 ) @ V_g_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_c ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5214]) ).
thf(5484,plain,
( ( ! [V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( class_Orderings_Oord @ T_c )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ T_c ) ) @ V_f_2 ) @ V_g_2 ) )
<=> ! [B_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_c ) @ ( hAPP @ V_f_2 @ B_x ) ) @ ( hAPP @ V_g_2 @ B_x ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5215]) ).
thf(5485,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5216]) ).
thf(5486,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( V_A_2 = V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5217]) ).
thf(5487,plain,
( ( ! [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_Ha_2 @ V_tsa_2 )
=> ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_G_Ha_2 )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_tsa_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5218]) ).
thf(5488,plain,
( ( ! [V_tsa_2: $i,V_ts_H_2: $i,V_G_2: $i,T_b: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_ts_H_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) @ V_tsa_2 ) @ V_ts_H_2 ) )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_tsa_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5219]) ).
thf(5489,plain,
( ( ! [V_G_2: $i,V_tsa_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) @ V_tsa_2 ) @ V_G_2 ) )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_tsa_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5220]) ).
thf(5490,plain,
( ( ! [V_g_2: $i,V_f_2: $i] :
( ! [B_x: $i] :
( ( hAPP @ V_f_2 @ B_x )
= ( hAPP @ V_g_2 @ B_x ) )
=> ( V_f_2 = V_g_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5221]) ).
thf(5491,plain,
( ( c_Hoare__Mirabelle_Ohoare__derivs @ t_a @ v_G_H @ v_ts )
= $true ),
inference(unfold_def,[status(thm)],[5222]) ).
thf(5492,plain,
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_HOL_Obool ) ) @ v_G_H ) @ sK1_B_G ) )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ t_a @ sK1_B_G @ v_ts ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5225]) ).
thf(5493,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_HOL_Obool ) ) @ v_G_H ) @ sK1_B_G ) )
= $true ),
inference(standard_cnf,[status(thm)],[5492]) ).
thf(5494,plain,
( ( c_Hoare__Mirabelle_Ohoare__derivs @ t_a @ sK1_B_G @ v_ts )
= $false ),
inference(standard_cnf,[status(thm)],[5492]) ).
thf(5495,plain,
( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ t_a @ sK1_B_G @ v_ts ) )
= $true ),
inference(polarity_switch,[status(thm)],[5494]) ).
thf(5496,plain,
( ( c_Hoare__Mirabelle_Ohoare__derivs @ t_a @ v_G_H @ v_ts )
= $true ),
inference(copy,[status(thm)],[5491]) ).
thf(5497,plain,
( ( ! [V_g_2: $i,V_f_2: $i] :
( ! [B_x: $i] :
( ( hAPP @ V_f_2 @ B_x )
= ( hAPP @ V_g_2 @ B_x ) )
=> ( V_f_2 = V_g_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5490]) ).
thf(5498,plain,
( ( ! [V_G_2: $i,V_tsa_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) @ V_tsa_2 ) @ V_G_2 ) )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_tsa_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5489]) ).
thf(5499,plain,
( ( ! [V_tsa_2: $i,V_ts_H_2: $i,V_G_2: $i,T_b: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_ts_H_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) @ V_tsa_2 ) @ V_ts_H_2 ) )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_tsa_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5488]) ).
thf(5500,plain,
( ( ! [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_Ha_2 @ V_tsa_2 )
=> ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_G_Ha_2 )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_tsa_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5487]) ).
thf(5501,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( V_A_2 = V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5486]) ).
thf(5502,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[5485]) ).
thf(5503,plain,
( ( ! [V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( class_Orderings_Oord @ T_c )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ T_c ) ) @ V_f_2 ) @ V_g_2 ) )
<=> ! [B_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_c ) @ ( hAPP @ V_f_2 @ B_x ) ) @ ( hAPP @ V_g_2 @ B_x ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5484]) ).
thf(5504,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( class_Orderings_Oord @ T_c )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ T_c ) ) @ V_f_2 ) @ V_g_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_c ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5483]) ).
thf(5505,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( class_Orderings_Oord @ T_c )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ T_c ) ) @ V_f_2 ) @ V_g_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_c ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5482]) ).
thf(5506,plain,
( ( ! [V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5481]) ).
thf(5507,plain,
( ( ! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5480]) ).
thf(5508,plain,
( ( ! [V_Q_2: $i,T_b: $i,V_x_2: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_P_2 ) @ V_Q_2 ) )
=> ( hBOOL @ ( hAPP @ V_Q_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5479]) ).
thf(5509,plain,
( ( ! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5478]) ).
thf(5510,plain,
( ( ! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5477]) ).
thf(5511,plain,
( ( ! [V_x_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_P_2 ) @ V_Q_2 ) )
=> ( ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_Q_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5476]) ).
thf(5512,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5475]) ).
thf(5513,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5474]) ).
thf(5514,plain,
( ( ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_z ) @ V_y ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_z ) @ V_x ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5473]) ).
thf(5515,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( V_x = V_y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5472]) ).
thf(5516,plain,
( ( ! [V_z: $i,V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_z ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5471]) ).
thf(5517,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) )
=> ( V_x = V_y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5470]) ).
thf(5518,plain,
( ( ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_b ) @ V_a ) )
=> ( ( V_b = V_c )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_c ) @ V_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5469]) ).
thf(5519,plain,
( ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oord @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_a ) @ V_b ) )
=> ( ( V_b = V_c )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_a ) @ V_c ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5468]) ).
thf(5520,plain,
( ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( V_a = V_b )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_c ) @ V_b ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_c ) @ V_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5467]) ).
thf(5521,plain,
( ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oord @ T_a )
=> ( ( V_a = V_b )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_b ) @ V_c ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_a ) @ V_c ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5466]) ).
thf(5522,plain,
( ( ! [V_x_2: $i,V_y_2: $i,T_b: $i] :
( ( class_Orderings_Oorder @ T_b )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_y_2 ) @ V_x_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_x_2 ) @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5465]) ).
thf(5523,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( V_x = V_y )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5464]) ).
thf(5524,plain,
( ( ! [V_y_2: $i,V_x_2: $i,T_b: $i] :
( ( class_Orderings_Oorder @ T_b )
=> ( ( V_x_2 = V_y_2 )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_x_2 ) @ V_y_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_y_2 ) @ V_x_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5463]) ).
thf(5525,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5462]) ).
thf(5526,plain,
( ( ! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5461]) ).
thf(5527,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ T_b @ V_A_2 ) ) @ ( c_Predicate_OPowp @ T_b @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5460]) ).
thf(5528,plain,
( ( ! [T_b: $i,V_g_2: $i,V_f_2: $i,T_c: $i] :
( ( class_Orderings_Oord @ T_c )
=> ( ! [B_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_c ) @ ( hAPP @ V_f_2 @ B_x ) ) @ ( hAPP @ V_g_2 @ B_x ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ T_c ) ) @ V_f_2 ) @ V_g_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5459]) ).
thf(5529,plain,
( ( ! [V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5458]) ).
thf(5530,plain,
( ( ! [V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5457]) ).
thf(5531,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5456]) ).
thf(5532,plain,
( ( ! [V_G_2: $i,T_b: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
= $true ),
inference(copy,[status(thm)],[5455]) ).
thf(5533,plain,
( ( ! [V_a_2: $i,T_b: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_a_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
= $true ),
inference(copy,[status(thm)],[5454]) ).
thf(5534,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ T_b ) @ V_A_2 ) ) @ ( hAPP @ ( c_Set_OPow @ T_b ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5453]) ).
thf(5535,plain,
( ( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_A_2 ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5452]) ).
thf(5536,plain,
( ( ! [V_x_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_x_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5451]) ).
thf(5537,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) )
<=> ( V_A_2 = V_B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5450]) ).
thf(5538,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) )
= V_A_2 ) )
= $true ),
inference(copy,[status(thm)],[5449]) ).
thf(5539,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5448]) ).
thf(5540,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5447]) ).
thf(5541,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_A_2 ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5446]) ).
thf(5542,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ( ~ ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5445]) ).
thf(5543,plain,
( ( ! [T_b: $i,V_A_2: $i,V_x_2: $i,V_B_2: $i] :
( ( ~ ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5444]) ).
thf(5544,plain,
( ( ! [T_b: $i,V_B_2: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ( ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5443]) ).
thf(5545,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ~ ( ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ~ ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5442]) ).
thf(5546,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
= V_A_2 ) )
= $true ),
inference(copy,[status(thm)],[5441]) ).
thf(5547,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
= V_A_2 ) )
= $true ),
inference(copy,[status(thm)],[5440]) ).
thf(5548,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5439]) ).
thf(5549,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5438]) ).
thf(5550,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5437]) ).
thf(5551,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5436]) ).
thf(5552,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5435]) ).
thf(5553,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5434]) ).
thf(5554,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5433]) ).
thf(5555,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5432]) ).
thf(5556,plain,
( ( ! [V_B_2: $i,T_b: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5431]) ).
thf(5557,plain,
( ( ! [V_A_2: $i,T_b: $i,V_x_2: $i,V_B_2: $i] :
( ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5430]) ).
thf(5558,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5429]) ).
thf(5559,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5428]) ).
thf(5560,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5427]) ).
thf(5561,plain,
( ( ! [V_A_2: $i,V_B_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5426]) ).
thf(5562,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5425]) ).
thf(5563,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5424]) ).
thf(5564,plain,
( ( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5423]) ).
thf(5565,plain,
( ( ! [V_B_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5422]) ).
thf(5566,plain,
( ( ! [V_D_2: $i,V_B_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_D_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5421]) ).
thf(5567,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5420]) ).
thf(5568,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5419]) ).
thf(5569,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5418]) ).
thf(5570,plain,
( ( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5417]) ).
thf(5571,plain,
( ( ! [V_B_2: $i,V_A_2: $i,V_C_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_A_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5416]) ).
thf(5572,plain,
( ( ! [V_D_2: $i,V_B_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_D_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5415]) ).
thf(5573,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_y_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ V_A_2 ) @ V_x_2 ) )
<=> ( ( V_y_2 = V_x_2 )
| ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5414]) ).
thf(5574,plain,
( ( ! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5413]) ).
thf(5575,plain,
( ( ! [V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5412]) ).
thf(5576,plain,
( ( ! [V_a_2: $i,V_D_2: $i,V_C_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_C_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_D_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5411]) ).
thf(5577,plain,
( ( ! [V_b_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5410]) ).
thf(5578,plain,
( ( ! [V_a_2: $i,V_B_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5409]) ).
thf(5579,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5408]) ).
thf(5580,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5407]) ).
thf(5581,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5406]) ).
thf(5582,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
| ( V_A_2 = V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5405]) ).
thf(5583,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
& ( V_A_2 != V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5404]) ).
thf(5584,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5403]) ).
thf(5585,plain,
( ( ! [V_A_2: $i,V_f_2: $i,T_c: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) ) )
<=> ? [B_AA: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) @ B_AA ) @ V_A_2 ) )
& ( V_B_2
= ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ B_AA ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5402]) ).
thf(5586,plain,
( ( ! [V_f_2: $i,T_c: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ T_b @ T_c @ V_f_2 ) @ V_A_2 ) ) @ ( hAPP @ ( c_Set_Oimage @ T_b @ T_c @ V_f_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5401]) ).
thf(5587,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_B_2 )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5400]) ).
thf(5588,plain,
( ( ! [V_A_2: $i,V_B_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_B_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5399]) ).
thf(5589,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5398]) ).
thf(5590,plain,
( ( ! [V_B_2: $i,V_D_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_D_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5397]) ).
thf(5591,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_A_2 ) )
= V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5396]) ).
thf(5592,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5395]) ).
thf(5593,plain,
( ( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5394]) ).
thf(5594,plain,
( ( ! [V_c_2: $i,T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_A_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_B_2 ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_B_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5393]) ).
thf(5595,plain,
( ( ! [V_c_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5392]) ).
thf(5596,plain,
( ( ! [V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5391]) ).
thf(5597,plain,
( ( ! [V_x_2: $i,T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5390]) ).
thf(5598,plain,
( ( ! [V_A_2: $i,T_b: $i,V_y_2: $i,V_x_2: $i] :
( ( V_x_2 = V_y_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_y_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5389]) ).
thf(5599,plain,
( ( ! [V_A_2: $i,T_b: $i,V_b_2: $i,V_a_2: $i] :
( ( V_a_2 = V_b_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_b_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5388]) ).
thf(5600,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5387]) ).
thf(5601,plain,
( ( ! [V_B_2: $i,V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5386]) ).
thf(5602,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5385]) ).
thf(5603,plain,
( ( ! [V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ ( hAPP @ V_f_2 @ V_x_2 ) )
= V_f_2 ) )
= $true ),
inference(copy,[status(thm)],[5384]) ).
thf(5604,plain,
( ( ! [T_b: $i,T_c: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 )
=> ( ( c_Fun_Ofun__upd @ T_c @ T_b @ V_f_2 @ V_x_2 @ V_y_2 )
= V_f_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5383]) ).
thf(5605,plain,
( ( ! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5382]) ).
thf(5606,plain,
( ( ! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
( ( ( V_z_2 = V_x_2 )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ V_y_2 ) @ V_z_2 )
= V_y_2 ) )
& ( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5381]) ).
thf(5607,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ T_c @ T_b @ V_f_2 @ V_x_2 @ V_y_2 ) @ V_x_2 )
= V_y_2 ) )
= $true ),
inference(copy,[status(thm)],[5380]) ).
thf(5608,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ V_y_2 )
= V_f_2 )
<=> ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5379]) ).
thf(5609,plain,
( ( ! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ T_b @ V_f_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5378]) ).
thf(5610,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_n ) @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[5377]) ).
thf(5611,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_m ) @ V_n ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_n ) @ V_m ) ) ) )
= $true ),
inference(copy,[status(thm)],[5376]) ).
thf(5612,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_m ) @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[5375]) ).
thf(5613,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_i ) @ V_j ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_j ) @ V_k ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_i ) @ V_k ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5374]) ).
thf(5614,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_m ) @ V_n ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_n ) @ V_m ) )
=> ( V_m = V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[5373]) ).
thf(5615,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofun__left__comm @ T_b @ T_c @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5372]) ).
thf(5616,plain,
( ( ! [V_n: $i] :
( V_n
!= ( hAPP @ c_Nat_OSuc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[5371]) ).
thf(5617,plain,
( ( ! [V_n: $i] :
( ( hAPP @ c_Nat_OSuc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[5370]) ).
thf(5618,plain,
( ( ! [V_nat_H_2: $i,V_nat_2: $i] :
( ( ( hAPP @ c_Nat_OSuc @ V_nat_2 )
= ( hAPP @ c_Nat_OSuc @ V_nat_H_2 ) )
<=> ( V_nat_2 = V_nat_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5369]) ).
thf(5619,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( ( hAPP @ c_Nat_OSuc @ V_x )
= ( hAPP @ c_Nat_OSuc @ V_y ) )
=> ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[5368]) ).
thf(5620,plain,
( ( ! [V_z_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ T_b @ T_c @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5367]) ).
thf(5621,plain,
( ( ! [V_x_2: $i,V_F_2: $i,V_g_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ T_b @ T_c @ V_f_2 @ V_z_2 @ V_g_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5366]) ).
thf(5622,plain,
( ( ! [V_w: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_w ) @ V_w ) ) )
= $true ),
inference(copy,[status(thm)],[5365]) ).
thf(5623,plain,
( ( ! [V_w: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_z ) @ V_w ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_w ) @ V_z ) ) ) )
= $true ),
inference(copy,[status(thm)],[5364]) ).
thf(5624,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_i ) @ V_j ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_j ) @ V_k ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_i ) @ V_k ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5363]) ).
thf(5625,plain,
( ( ! [V_w: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_z ) @ V_w ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_w ) @ V_z ) )
=> ( V_z = V_w ) ) ) )
= $true ),
inference(copy,[status(thm)],[5362]) ).
thf(5626,plain,
( ( ! [T_f: $i,T_e: $i,T_d: $i,T_b: $i,T_c: $i,V_x_H_2: $i,V_g_H_2: $i,V_f_H_2: $i,V_x_2: $i,V_g_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) )
= ( hAPP @ V_f_H_2 @ ( hAPP @ V_g_H_2 @ V_x_H_2 ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_b @ T_f @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5361]) ).
thf(5627,plain,
( ( ! [V_v_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= V_c_2 )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ V_v_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5360]) ).
thf(5628,plain,
( ( ! [V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
=> ! [B_v: $i] :
( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5359]) ).
thf(5629,plain,
( ( ! [V_v_2: $i,V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5358]) ).
thf(5630,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5357]) ).
thf(5631,plain,
( ( ! [V_h_2: $i,V_g_2: $i,T_e: $i,V_f_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_f_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_d @ T_b @ V_g_2 ) @ V_h_2 ) )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_e @ V_f_2 ) @ V_g_2 ) ) @ V_h_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5356]) ).
thf(5632,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5355]) ).
thf(5633,plain,
( ( ! [V_b_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_a_2: $i,V_x_2: $i] :
( ( ( V_x_2 = V_a_2 )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_a_2 @ V_b_2 ) @ V_x_2 )
= V_b_2 ) )
& ( ( V_x_2 != V_a_2 )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_a_2 @ V_b_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5354]) ).
thf(5634,plain,
( ( ! [T_c: $i,T_b: $i,V_A_2: $i,V_y_2: $i,V_x_2: $i,V_B_2: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5353]) ).
thf(5635,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5352]) ).
thf(5636,plain,
( ( ! [T_c: $i,T_b: $i,V_B_2: $i,V_y_2: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5351]) ).
thf(5637,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5350]) ).
thf(5638,plain,
( ( ! [V_y_2: $i,V_x_2: $i,T_c: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_x_2 ) @ V_y_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5349]) ).
thf(5639,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_Q_2: $i,V_P_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_P_2 ) @ V_Q_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_2 @ V_x_2 ) @ V_y_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5348]) ).
thf(5640,plain,
( ( ! [V_Q_2: $i,T_c: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_P_2 ) @ V_Q_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_2 @ V_x_2 ) @ V_y_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5347]) ).
thf(5641,plain,
( ( ! [V_A_2: $i,T_c: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_B_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5346]) ).
thf(5642,plain,
( ( ! [V_B_2: $i,T_c: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5345]) ).
thf(5643,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5344]) ).
thf(5644,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5343]) ).
thf(5645,plain,
( ( ! [T_c: $i,T_b: $i,V_P_2: $i] :
( ! [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
<=> ! [B_a: $i,B_b: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ B_a ) @ B_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5342]) ).
thf(5646,plain,
( ( ! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_c: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_H_2 ) @ V_b_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_b_2 = V_b_H_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5341]) ).
thf(5647,plain,
( ( ! [V_b_H: $i,V_a_H: $i,V_b: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_H ) @ V_b_H ) )
=> ~ ( ( V_a = V_a_H )
=> ( V_b != V_b_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[5340]) ).
thf(5648,plain,
( ( ! [V_c_2: $i,T_d: $i,T_c: $i,T_b: $i,V_q_2: $i,V_p_2: $i] :
( ( V_p_2 = V_q_2 )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_p_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5339]) ).
thf(5649,plain,
( ( ! [V_qr_H: $i,V_qr: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr_H ) )
=> ( V_qr = V_qr_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[5338]) ).
thf(5650,plain,
( ( ! [V_R2_2: $i,V_R1_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_R1_2 ) @ V_R2_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ T_b @ V_R2_2 ) ) @ ( c_Wellfounded_Oaccp @ T_b @ V_R1_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5337]) ).
thf(5651,plain,
( ( ! [V_a_2: $i,V_b_2: $i,V_r_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_b_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_a_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5336]) ).
thf(5652,plain,
( ( ! [V_a_2: $i,V_r_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_a_2 ) )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ B_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5335]) ).
thf(5653,plain,
( ( ! [V_a_2: $i,V_r_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_a_2 ) )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ B_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5334]) ).
thf(5654,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ( ( hAPP @ c_Int_ORep__Integ @ V_x_2 )
= ( hAPP @ c_Int_ORep__Integ @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5333]) ).
thf(5655,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_z_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5332]) ).
thf(5656,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5331]) ).
thf(5657,plain,
( ( ! [V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5330]) ).
thf(5658,plain,
( ( ! [V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
<=> ! [B_x: $i,B_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_y ) )
<=> ( ( hAPP @ V_R_2 @ B_x )
= ( hAPP @ V_R_2 @ B_y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5329]) ).
thf(5659,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
( ( c_Typedef_Otype__definition @ T_b @ T_c @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( hAPP @ V_Abs_2 @ ( hAPP @ V_Rep_2 @ V_x_2 ) )
= V_x_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5328]) ).
thf(5660,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
( ( c_Typedef_Otype__definition @ T_b @ T_c @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( ( hAPP @ V_Rep_2 @ V_x_2 )
= ( hAPP @ V_Rep_2 @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5327]) ).
thf(5661,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ T_b @ T_c @ V_f_2 ) @ V_A_2 ) @ V_x_2 ) )
<=> ( hBOOL @ ( hAPP @ V_A_2 @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5326]) ).
thf(5662,plain,
( ( ! [V_f_2: $i,T_c: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) ) @ ( hAPP @ ( c_Set_Ovimage @ T_c @ T_b @ V_f_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5325]) ).
thf(5663,plain,
( ( ! [V_P_2: $i,T_b: $i] :
( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 )
= V_P_2 ) )
= $true ),
inference(copy,[status(thm)],[5324]) ).
thf(5664,plain,
( ( ! [V_x_1: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x_1 )
= V_x_1 ) )
= $true ),
inference(copy,[status(thm)],[5323]) ).
thf(5665,plain,
( ( ! [V_x_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Predicate_Oreflp @ T_b @ V_r_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5322]) ).
thf(5666,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[5321]) ).
thf(5667,plain,
( ( ! [V_T_2: $i,V_S_2: $i,V_R_2: $i,T_e: $i,T_c: $i,T_d: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_d @ T_c ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_d ) @ V_R_2 ) @ V_S_2 ) ) @ V_T_2 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_c ) @ V_R_2 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_e @ T_d @ T_c ) @ V_S_2 ) @ V_T_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5320]) ).
thf(5668,plain,
( ( ! [T_d: $i,T_c: $i,T_b: $i,V_c_2: $i,V_s_2: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ V_b_2 ) @ V_c_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ T_b @ T_c @ T_d @ V_r_2 @ V_s_2 ) @ V_a_2 ) @ V_c_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5319]) ).
thf(5669,plain,
( ( ! [T_c: $i,T_b: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_b @ T_c @ V_r_2 ) @ V_b_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5318]) ).
thf(5670,plain,
( ( ! [V_a3_2: $i,V_a1_2: $i,V_s_2: $i,V_r_2: $i,T_d: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ T_b @ T_c @ T_d @ V_r_2 @ V_s_2 ) @ V_a1_2 ) @ V_a3_2 ) )
<=> ? [B_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_b ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ B_b ) @ V_a3_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5317]) ).
thf(5671,plain,
( ( ! [V_a2_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_b @ T_c @ V_r_2 ) @ V_a2_2 ) )
<=> ? [B_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_a ) @ V_a2_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5316]) ).
thf(5672,plain,
( ( ! [T_c: $i,T_b: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_b @ T_c @ V_r_2 ) @ V_a_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5315]) ).
thf(5673,plain,
( ( ! [V_a1_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_b @ T_c @ V_r_2 ) @ V_a1_2 ) )
<=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_x1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5314]) ).
thf(5674,plain,
( ( ! [V_p_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Wellfounded_OwfP @ T_b @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_p_2 ) @ V_r_2 ) )
=> ( c_Wellfounded_OwfP @ T_b @ V_p_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5313]) ).
thf(5675,plain,
( ( ! [T_b: $i,V_c_2: $i,V_P_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
=> ( ( V_c_2
= ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ V_c_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5312]) ).
thf(5676,plain,
( ( ! [T_b: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) ) )
<=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5311]) ).
thf(5677,plain,
( ( ! [T_b: $i,V_P_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5310]) ).
thf(5678,plain,
( ( ! [T_b: $i,B_P: $i] :
( ? [B_x: $i] : ( hBOOL @ ( hAPP @ B_P @ B_x ) )
=> ( hBOOL @ ( hAPP @ B_P @ ( c_Hilbert__Choice_OEps @ T_b @ B_P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5309]) ).
thf(5679,plain,
( ( ! [T_b: $i,V_x_2: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5308]) ).
thf(5680,plain,
( ( ! [V_r_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_c @ T_b ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_c ) @ V_r_2 ) )
= V_r_2 ) )
= $true ),
inference(copy,[status(thm)],[5307]) ).
thf(5681,plain,
( ( ! [V_x_2: $i,V_n_2: $i,T_b: $i,V_f_2: $i] :
( ( hAPP @ V_f_2 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_n_2 ) @ V_f_2 ) @ V_x_2 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_n_2 ) @ V_f_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5306]) ).
thf(5682,plain,
( ( ! [V_list_H_2: $i,V_a_H_2: $i,V_list_2: $i,V_a_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_2 ) @ V_list_2 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_H_2 ) @ V_list_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_list_2 = V_list_H_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5305]) ).
thf(5683,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs )
!= V_xs ) )
= $true ),
inference(copy,[status(thm)],[5304]) ).
thf(5684,plain,
( ( ! [V_x: $i,T_a: $i,V_xs: $i] :
( V_xs
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs ) ) )
= $true ),
inference(copy,[status(thm)],[5303]) ).
thf(5685,plain,
( ( ! [V_x_H: $i,V_x: $i,V_xs: $i,T_a: $i,V_i_H: $i,V_i: $i] :
( ( V_i != V_i_H )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i_H ) @ V_x_H )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i_H ) @ V_x_H ) ) @ V_i ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[5302]) ).
thf(5686,plain,
( ( ! [V_y: $i,V_x: $i,V_i: $i,V_xs: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_y ) ) )
= $true ),
inference(copy,[status(thm)],[5301]) ).
thf(5687,plain,
( ( ! [V_zs: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys ) ) @ V_zs )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_ys ) @ V_zs ) ) ) )
= $true ),
inference(copy,[status(thm)],[5300]) ).
thf(5688,plain,
( ( ! [V_tsa_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_tsa_2 ) )
<=> ? [B_us: $i] :
( ( ( V_xs_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ B_us ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ys_2 )
= V_tsa_2 ) )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ B_us )
= V_zs_2 )
& ( V_ys_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_tsa_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5299]) ).
thf(5689,plain,
( ( ! [V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_zs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5298]) ).
thf(5690,plain,
( ( ! [V_zs_2: $i,V_xs_2: $i,V_ys_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_ys_2 ) @ V_xs_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_xs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5297]) ).
thf(5691,plain,
( ( ! [V_us: $i,V_ys: $i,V_zs: $i,V_xs1: $i,V_xs: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_xs1 )
= V_zs )
=> ( ( V_ys
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs1 ) @ V_us ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs ) @ V_us ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5296]) ).
thf(5692,plain,
( ( ! [V_m_2: $i,V_n_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Oof__nat @ V_n_2 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ V_m_2 ) )
<=> ( V_n_2 = V_m_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5295]) ).
thf(5693,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_x_2 )
= ( hAPP @ c_Code__Numeral_Onat__of @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5294]) ).
thf(5694,plain,
( ( ! [V_l_2: $i,V_k_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_k_2 )
= ( hAPP @ c_Code__Numeral_Onat__of @ V_l_2 ) )
<=> ( V_k_2 = V_l_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5293]) ).
thf(5695,plain,
( ( ! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
= ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) )
<=> ( V_xs_2 = V_ys_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5292]) ).
thf(5696,plain,
( ( ! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
= V_ys_2 )
<=> ( V_xs_2
= ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5291]) ).
thf(5697,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( hAPP @ ( c_List_Orev @ T_a ) @ ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs ) )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[5290]) ).
thf(5698,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_a_2 ) @ V_b_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_b_2 ) @ V_a_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5289]) ).
thf(5699,plain,
( ( ! [V_a1_2: $i,V_a2_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_a2_2 ) @ V_a1_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ V_a2_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5288]) ).
thf(5700,plain,
( ( ! [T_c: $i,T_b: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_b_2 ) @ V_a_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5287]) ).
thf(5701,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_b_2 ) @ V_a_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5286]) ).
thf(5702,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Predicate_Otransp @ T_b @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_y_2 ) @ V_z_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5285]) ).
thf(5703,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Predicate_Osymp @ T_b @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_y_2 ) @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5284]) ).
thf(5704,plain,
( ( ! [V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Opart__equivp @ T_b @ V_R_2 )
<=> ( ? [B_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_x ) )
& ! [B_x: $i,B_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_y ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_x ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_y ) @ B_y ) )
& ( ( hAPP @ V_R_2 @ B_x )
= ( hAPP @ V_R_2 @ B_y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5283]) ).
thf(5705,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Opart__equivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5282]) ).
thf(5706,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Opart__equivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_z_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5281]) ).
thf(5707,plain,
( ( ! [V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ T_b @ V_R_2 ) @ V_x_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5280]) ).
thf(5708,plain,
( ( class_Lattices_Obounded__lattice @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5279]) ).
thf(5709,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Obounded__lattice @ T_1 )
=> ( class_Lattices_Obounded__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5278]) ).
thf(5710,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ T_1 )
=> ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5277]) ).
thf(5711,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Odistrib__lattice @ T_1 )
=> ( class_Lattices_Odistrib__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5276]) ).
thf(5712,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Oboolean__algebra @ T_1 )
=> ( class_Lattices_Oboolean__algebra @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5275]) ).
thf(5713,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ T_1 )
=> ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5274]) ).
thf(5714,plain,
( ( ! [T_1: $i,T_2: $i] :
( ( ( class_Finite__Set_Ofinite @ T_2 )
& ( class_Finite__Set_Ofinite @ T_1 ) )
=> ( class_Finite__Set_Ofinite @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5273]) ).
thf(5715,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olattice @ T_1 )
=> ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5272]) ).
thf(5716,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ T_1 )
=> ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5271]) ).
thf(5717,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Otop @ T_1 )
=> ( class_Orderings_Otop @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5270]) ).
thf(5718,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oord @ T_1 )
=> ( class_Orderings_Oord @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5269]) ).
thf(5719,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Obot @ T_1 )
=> ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5268]) ).
thf(5720,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Groups_Ouminus @ T_1 )
=> ( class_Groups_Ouminus @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5267]) ).
thf(5721,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Groups_Ominus @ T_1 )
=> ( class_Groups_Ominus @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5266]) ).
thf(5722,plain,
( ( ! [T_1: $i,T_2: $i] :
( ( ( class_Enum_Oenum @ T_2 )
& ( class_Enum_Oenum @ T_1 ) )
=> ( class_Enum_Oenum @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5265]) ).
thf(5723,plain,
( ( class_Complete__Lattice_Ocomplete__lattice @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5264]) ).
thf(5724,plain,
( ( class_Lattices_Obounded__lattice__top @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5263]) ).
thf(5725,plain,
( ( class_Lattices_Obounded__lattice__bot @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5262]) ).
thf(5726,plain,
( ( class_Lattices_Osemilattice__sup @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5261]) ).
thf(5727,plain,
( ( class_Lattices_Osemilattice__inf @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5260]) ).
thf(5728,plain,
( ( class_Lattices_Odistrib__lattice @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5259]) ).
thf(5729,plain,
( ( class_Lattices_Oboolean__algebra @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5258]) ).
thf(5730,plain,
( ( class_Orderings_Opreorder @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5257]) ).
thf(5731,plain,
( ( class_Finite__Set_Ofinite @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5256]) ).
thf(5732,plain,
( ( class_Lattices_Olattice @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5255]) ).
thf(5733,plain,
( ( class_Orderings_Oorder @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5254]) ).
thf(5734,plain,
( ( class_Orderings_Otop @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5253]) ).
thf(5735,plain,
( ( class_Orderings_Oord @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5252]) ).
thf(5736,plain,
( ( class_Orderings_Obot @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5251]) ).
thf(5737,plain,
( ( class_Groups_Ouminus @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5250]) ).
thf(5738,plain,
( ( class_Groups_Ominus @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5249]) ).
thf(5739,plain,
( ( class_Enum_Oenum @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5248]) ).
thf(5740,plain,
( ( class_Nat_Osize @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5247]) ).
thf(5741,plain,
( ( ! [T_1: $i] : ( class_Nat_Osize @ ( tc_Hoare__Mirabelle_Otriple @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[5246]) ).
thf(5742,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
= V_P ) )
= $true ),
inference(copy,[status(thm)],[5245]) ).
thf(5743,plain,
( ( ! [V_Q: $i,V_P: $i,T_b: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ T_a @ T_b ) @ V_P ) @ V_Q )
= V_P ) )
= $true ),
inference(copy,[status(thm)],[5244]) ).
thf(5744,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_c @ T_b @ T_d ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ V_P_2 @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5243]) ).
thf(5745,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_c @ T_d @ T_b ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ V_Q_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5242]) ).
thf(5746,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_c @ T_d @ T_b ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5241]) ).
thf(5747,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) )
| ( V_x_2 = V_y_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5240]) ).
thf(5748,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5239]) ).
thf(5749,plain,
( ( ~ ( hBOOL @ c_fFalse ) )
= $true ),
inference(copy,[status(thm)],[5238]) ).
thf(5750,plain,
( ( hBOOL @ c_fTrue )
= $true ),
inference(copy,[status(thm)],[5237]) ).
thf(5751,plain,
( ( ! [V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) )
| ~ ( hBOOL @ V_P_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5236]) ).
thf(5752,plain,
( ( ! [V_P_2: $i] :
( ~ ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5235]) ).
thf(5753,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ V_P_2 )
| ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5234]) ).
thf(5754,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_P_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5233]) ).
thf(5755,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5232]) ).
thf(5756,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5231]) ).
thf(5757,plain,
( ( ! [V_P_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5230]) ).
thf(5758,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_P_2 )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5229]) ).
thf(5759,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5228]) ).
thf(5760,plain,
( ( ! [V_P_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5227]) ).
thf(5761,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) )
| ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5226]) ).
thf(5762,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_HOL_Obool ) ) @ v_G_H ) @ sK1_B_G ) )
= $true ),
inference(copy,[status(thm)],[5493]) ).
thf(5763,plain,
( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ t_a @ sK1_B_G @ v_ts ) )
= $true ),
inference(copy,[status(thm)],[5495]) ).
thf(5764,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5570]) ).
thf(5765,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ SX3 @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ SX1 @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) @ SX3 ) @ SX1 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5544]) ).
thf(5766,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5558]) ).
thf(5767,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 )
= SX0 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 )
!= SX0 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5562]) ).
thf(5768,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Olinorder @ SX2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5525]) ).
thf(5769,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SX3 @ SX2 @ SX1 ) @ SX0 ) )
| ~ ! [SX4: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX4 ) @ SX0 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX4 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SX3 @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5671]) ).
thf(5770,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( c_Equiv__Relations_Opart__equivp @ SX1 @ SX0 )
| ~ ( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX3 ) @ SX3 ) ) )
| ( ( hAPP @ SX0 @ SX2 )
!= ( hAPP @ SX0 @ SX3 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX3 ) @ SX3 ) ) )
| ( ( hAPP @ SX0 @ SX2 )
!= ( hAPP @ SX0 @ SX3 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX3 ) @ SX3 ) ) )
| ( ( hAPP @ SX0 @ SX2 )
!= ( hAPP @ SX0 @ SX3 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX3 ) @ SX3 ) ) )
| ( ( hAPP @ SX0 @ SX2 )
!= ( hAPP @ SX0 @ SX3 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) ) ) ) )
| ( c_Equiv__Relations_Opart__equivp @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5704]) ).
thf(5771,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX2 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5597]) ).
thf(5772,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Orderings_Otop @ SX1 )
| ( class_Orderings_Otop @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5717]) ).
thf(5773,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i,SX8: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SX8 @ SX7 @ SX6 @ SX5 ) @ SX4 )
!= ( hAPP @ ( c_Fun_Ocomp @ SX3 @ SX7 @ SX6 @ SX2 ) @ SX1 ) )
| ( ( hAPP @ SX5 @ ( hAPP @ SX4 @ SX0 ) )
= ( hAPP @ SX2 @ ( hAPP @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5629]) ).
thf(5774,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Orderings_Oord @ SX3 )
| ~ ! [SX4: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ ( hAPP @ SX2 @ SX4 ) ) @ ( hAPP @ SX1 @ SX4 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX0 @ SX3 ) ) @ SX2 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5528]) ).
thf(5775,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX5 @ SX4 ) @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX4 ) @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX1 @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) ) @ SX5 ) @ SX2 ) @ SX4 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5636]) ).
thf(5776,plain,
( ( ! [SX0: $i] :
( SX0
!= ( hAPP @ c_Nat_OSuc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5616]) ).
thf(5777,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX2 != SX1 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) @ SX1 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5526]) ).
thf(5778,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ SX2 @ SX1 ) ) @ ( c_Predicate_OPowp @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5527]) ).
thf(5779,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5748]) ).
thf(5780,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SX2 @ SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5657]) ).
thf(5781,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SX1 )
| ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5710]) ).
thf(5782,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SX3 @ SX2 @ SX1 )
| ( ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5609]) ).
thf(5783,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SX1 )
!= ( hAPP @ c_Nat_OSuc @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5619]) ).
thf(5784,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX3 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ SX1 @ SX4 @ SX0 ) @ SX3 ) ) @ ( hAPP @ ( c_Set_Ovimage @ SX1 @ SX4 @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5662]) ).
thf(5785,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ! [SX3: $i] :
~ ( hBOOL @ ( hAPP @ SX2 @ SX3 ) )
| ( SX1
!= ( c_Hilbert__Choice_OEps @ SX0 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5675]) ).
thf(5786,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX2 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5594]) ).
thf(5787,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5579]) ).
thf(5788,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX5 @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) ) @ SX3 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5639]) ).
thf(5789,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SX1 )
!= ( hAPP @ c_Int_ORep__Integ @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( hAPP @ c_Int_ORep__Integ @ SX1 )
= ( hAPP @ c_Int_ORep__Integ @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5654]) ).
thf(5790,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( ( SX5 != SX4 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SX3 @ SX2 @ SX1 @ SX4 @ SX0 ) @ SX5 )
= ( hAPP @ SX1 @ SX5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5605]) ).
thf(5791,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SX2 ) @ SX1 )
!= ( hAPP @ ( c_List_Orev @ SX2 ) @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( hAPP @ ( c_List_Orev @ SX2 ) @ SX1 )
= ( hAPP @ ( c_List_Orev @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5695]) ).
thf(5792,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SX3 @ SX2 @ SX1 ) @ SX0 ) )
| ~ ! [SX4: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX4 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX4 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SX3 @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5673]) ).
thf(5793,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SX2 ) @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( c_Hoare__Mirabelle_Ohoare__derivs @ SX2 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5498]) ).
thf(5794,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Groups_Ouminus @ SX1 )
| ( class_Groups_Ouminus @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5720]) ).
thf(5795,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX3 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX3 ) @ SX1 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5566]) ).
thf(5796,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SX1 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SX1 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5694]) ).
thf(5797,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX5 @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) ) @ SX3 ) @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5643]) ).
thf(5798,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5581]) ).
thf(5799,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ SX1 @ ( hAPP @ SX2 @ SX0 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SX1 @ ( hAPP @ SX2 @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5661]) ).
thf(5800,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i,SX8: $i,SX9: $i,SX10: $i] :
( ( ( hAPP @ SX10 @ ( hAPP @ SX9 @ SX8 ) )
!= ( hAPP @ SX7 @ ( hAPP @ SX6 @ SX5 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SX4 @ SX3 @ SX2 @ SX10 ) @ SX9 ) @ SX8 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SX1 @ SX3 @ SX0 @ SX7 ) @ SX6 ) @ SX5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5626]) ).
thf(5801,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) @ SX1 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5540]) ).
thf(5802,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SX5 @ SX4 @ SX3 )
| ( ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
= ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5615]) ).
thf(5803,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX0 ) )
| ! [SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX3 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX3 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX3 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX3 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5653]) ).
thf(5804,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5569]) ).
thf(5805,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SX4 @ SX3 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5706]) ).
thf(5806,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Orderings_Opreorder @ SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX1 ) @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5502]) ).
thf(5807,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Lattices_Olattice @ SX1 )
| ( class_Lattices_Olattice @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5715]) ).
thf(5808,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SX1 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX1 @ ( c_Hilbert__Choice_OEps @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5677]) ).
thf(5809,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX4 @ SX3 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SX1 @ SX0 @ SX4 ) @ SX2 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5700]) ).
thf(5810,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ( ( c_Fun_Ofun__upd @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 )
!= SX2 )
| ( ( hAPP @ SX2 @ SX1 )
= SX0 ) )
| ~ ( ( ( hAPP @ SX2 @ SX1 )
!= SX0 )
| ( ( c_Fun_Ofun__upd @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 )
= SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5608]) ).
thf(5811,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ SX2 ) @ SX1 ) ) @ ( hAPP @ ( c_Set_OPow @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5534]) ).
thf(5812,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX0 ) )
| ! [SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX3 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX3 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX3 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX3 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5652]) ).
thf(5813,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Predicate_Osymp @ SX3 @ SX2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5703]) ).
thf(5814,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
~ ( ~ ( ( SX5 != SX4 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SX3 @ SX2 @ SX1 @ SX4 @ SX0 ) @ SX5 )
= SX0 ) )
| ~ ( ~ ( ( SX5 != SX4 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SX3 @ SX2 @ SX1 @ SX4 @ SX0 ) @ SX5 )
= ( hAPP @ SX1 @ SX5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5606]) ).
thf(5815,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SX2 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5592]) ).
thf(5816,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( class_Enum_Oenum @ SX1 )
| ~ ( class_Enum_Oenum @ SX0 ) )
| ( class_Enum_Oenum @ ( tc_fun @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5722]) ).
thf(5817,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SX5 @ SX4 ) @ SX3 ) @ SX2 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SX5 @ SX4 ) @ SX1 ) @ SX0 ) )
| ~ ( ( SX3 != SX1 )
| ( SX2 != SX0 ) ) )
| ~ ( ~ ~ ( ( SX3 != SX1 )
| ( SX2 != SX0 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SX5 @ SX4 ) @ SX3 ) @ SX2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SX5 @ SX4 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5646]) ).
thf(5818,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SX0 ) @ SX1 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5625]) ).
thf(5819,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX5 @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) ) @ SX3 ) @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5644]) ).
thf(5820,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( SX1 = SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5582]) ).
thf(5821,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Orderings_Oord @ SX3 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ SX3 ) ) @ SX1 ) @ SX0 ) )
| ! [SX4: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ ( hAPP @ SX1 @ SX4 ) ) @ ( hAPP @ SX0 @ SX4 ) ) ) )
| ~ ( ~ ! [SX4: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ ( hAPP @ SX1 @ SX4 ) ) @ ( hAPP @ SX0 @ SX4 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ SX3 ) ) @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5503]) ).
thf(5822,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ SX2 @ SX1 ) )
| ( hBOOL @ ( hAPP @ SX2 @ ( c_Hilbert__Choice_OEps @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5679]) ).
thf(5823,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SX1 @ ( c_Hilbert__Choice_OEps @ SX0 @ SX1 ) ) )
| ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SX1 @ SX2 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SX1 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX1 @ ( c_Hilbert__Choice_OEps @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5676]) ).
thf(5824,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ( hAPP @ SX1 @ SX2 )
= ( hAPP @ SX0 @ SX2 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5497]) ).
thf(5825,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_Fun_Oinj__on @ SX4 @ SX3 @ SX2 @ SX1 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX0 ) @ SX1 ) )
| ( c_Fun_Oinj__on @ SX4 @ SX3 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5588]) ).
thf(5826,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Orderings_Oord @ SX3 )
| ( SX2 != SX1 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5521]) ).
thf(5827,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SX6 @ SX5 @ SX4 @ SX3 ) @ SX2 )
!= SX1 )
| ( ( hAPP @ SX3 @ ( hAPP @ SX2 @ SX0 ) )
= ( hAPP @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5627]) ).
thf(5828,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
~ ( ~ ( ( SX5 != SX4 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SX3 @ SX2 @ SX1 @ SX4 @ SX0 ) @ SX5 )
= SX0 ) )
| ~ ( ~ ( ( SX5 != SX4 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SX3 @ SX2 @ SX1 @ SX4 @ SX0 ) @ SX5 )
= ( hAPP @ SX1 @ SX5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5633]) ).
thf(5829,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX3 ) @ SX2 ) @ SX1 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX3 ) @ SX2 ) @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX3 ) @ SX2 ) @ SX1 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX3 ) @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5689]) ).
thf(5830,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Orderings_Opreorder @ SX3 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5516]) ).
thf(5831,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX3 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX2 ) @ SX0 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX3 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5598]) ).
thf(5832,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX5 ) @ SX4 ) @ SX3 )
!= SX2 )
| ( SX1
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX5 ) @ SX3 ) @ SX0 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX5 ) @ SX4 ) @ SX1 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX5 ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5691]) ).
thf(5833,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX3 ) @ SX2 ) @ SX1 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX3 ) @ SX0 ) @ SX1 ) )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX3 ) @ SX2 ) @ SX1 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX3 ) @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5690]) ).
thf(5834,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ SX2 @ SX0 ) )
| ( hBOOL @ ( hAPP @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5511]) ).
thf(5835,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SX3 @ SX2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5705]) ).
thf(5836,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SX3 @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SX3 @ SX2 ) @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5649]) ).
thf(5837,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX1 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SX0 @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5596]) ).
thf(5838,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ SX2 @ SX0 ) ) @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5650]) ).
thf(5839,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5539]) ).
thf(5840,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX4 @ SX3 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SX1 @ SX0 @ SX4 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5669]) ).
thf(5841,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SX1 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SX1 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5692]) ).
thf(5842,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX5 @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) ) @ SX3 ) @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5637]) ).
thf(5843,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5571]) ).
thf(5844,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2 != SX1 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) @ SX1 ) @ SX2 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) @ SX1 ) @ SX2 ) ) )
| ( SX2 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5507]) ).
thf(5845,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ SX0 ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5535]) ).
thf(5846,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ SX3 @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) @ SX3 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5508]) ).
thf(5847,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5512]) ).
thf(5848,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5624]) ).
thf(5849,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ SX3 @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) @ SX3 ) @ SX0 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5556]) ).
thf(5850,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Orderings_Oord @ SX4 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ SX4 ) ) @ SX2 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX4 ) @ ( hAPP @ SX2 @ SX0 ) ) @ ( hAPP @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5505]) ).
thf(5851,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX4 @ SX3 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SX1 @ SX0 @ SX4 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5672]) ).
thf(5852,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SX5 @ SX4 ) @ SX3 ) @ SX2 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SX5 @ SX4 ) @ SX1 ) @ SX0 ) )
| ~ ( ( SX3 != SX1 )
| ( SX2 != SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5647]) ).
thf(5853,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX0 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5595]) ).
thf(5854,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX0 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5600]) ).
thf(5855,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX5 @ SX4 ) @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX4 ) @ SX3 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX1 @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) ) @ SX2 ) @ SX5 ) @ SX4 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5634]) ).
thf(5856,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ~ ( ( SX1 != SX0 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ~ ( ( SX1 != SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5583]) ).
thf(5857,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX0 ) @ SX2 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5576]) ).
thf(5858,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Orderings_Oord @ SX1 )
| ( class_Orderings_Oord @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5718]) ).
thf(5859,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5699]) ).
thf(5860,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_Predicate_Otransp @ SX4 @ SX3 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5702]) ).
thf(5861,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 )
!= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5537]) ).
thf(5862,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Orderings_Oord @ SX4 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ SX4 ) ) @ SX2 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX4 ) @ ( hAPP @ SX2 @ SX0 ) ) @ ( hAPP @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5504]) ).
thf(5863,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Orderings_Oorder @ SX3 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX0 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5514]) ).
thf(5864,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SX1 )
!= ( hAPP @ c_Nat_OSuc @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( hAPP @ c_Nat_OSuc @ SX1 )
= ( hAPP @ c_Nat_OSuc @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5618]) ).
thf(5865,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX3 @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX3 @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5651]) ).
thf(5866,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Orderings_Oord @ SX3 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX2 ) @ SX1 ) )
| ( SX1 != SX0 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5519]) ).
thf(5867,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5559]) ).
thf(5868,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5563]) ).
thf(5869,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX3 ) @ ( hAPP @ ( c_Set_Oimage @ SX2 @ SX4 @ SX1 ) @ SX0 ) ) )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX5 ) @ SX0 ) )
| ( SX3
!= ( hAPP @ ( c_Set_Oimage @ SX2 @ SX4 @ SX1 ) @ SX5 ) ) ) )
| ~ ( ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX5 ) @ SX0 ) )
| ( SX3
!= ( hAPP @ ( c_Set_Oimage @ SX2 @ SX4 @ SX1 ) @ SX5 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX3 ) @ ( hAPP @ ( c_Set_Oimage @ SX2 @ SX4 @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5585]) ).
thf(5870,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( SX5 != SX4 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SX3 @ SX2 @ SX1 ) @ SX0 ) @ SX5 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SX3 @ SX2 @ SX1 ) @ SX0 ) @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5648]) ).
thf(5871,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SX3 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX1 @ SX2 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) @ SX1 ) @ SX3 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5543]) ).
thf(5872,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX0 ) @ SX2 ) )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5591]) ).
thf(5873,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Olinorder @ SX2 )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5513]) ).
thf(5874,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ SX3 @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) @ SX0 ) @ SX3 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5557]) ).
thf(5875,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SX1 )
| ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5711]) ).
thf(5876,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Groups_Ominus @ SX1 )
| ( class_Groups_Ominus @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5721]) ).
thf(5877,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX0 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5602]) ).
thf(5878,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX3 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX3 ) @ SX1 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5572]) ).
thf(5879,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( ( SX5 != SX4 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SX3 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SX3 @ SX2 ) @ SX5 ) @ SX1 ) ) @ SX4 ) @ SX0 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SX3 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SX3 @ SX2 ) @ SX4 ) @ SX0 ) ) @ SX5 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5685]) ).
thf(5880,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX3 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ SX4 @ SX1 @ SX0 ) @ SX3 ) ) @ ( hAPP @ ( c_Set_Oimage @ SX4 @ SX1 @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5586]) ).
thf(5881,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5698]) ).
thf(5882,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SX1 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SX1 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5693]) ).
thf(5883,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SX7 @ SX6 @ SX5 @ SX4 ) @ SX3 )
!= ( hAPP @ ( c_Fun_Ocomp @ SX2 @ SX6 @ SX5 @ SX1 ) @ SX0 ) )
| ! [SX8: $i] :
( ( hAPP @ SX4 @ ( hAPP @ SX3 @ SX8 ) )
= ( hAPP @ SX1 @ ( hAPP @ SX0 @ SX8 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5628]) ).
thf(5884,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) )
| ( ( hAPP @ SX0 @ SX2 )
= ( hAPP @ SX0 @ SX3 ) ) )
| ~ ( ( ( hAPP @ SX0 @ SX2 )
!= ( hAPP @ SX0 @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) ) ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) )
| ( ( hAPP @ SX0 @ SX2 )
= ( hAPP @ SX0 @ SX3 ) ) )
| ~ ( ( ( hAPP @ SX0 @ SX2 )
!= ( hAPP @ SX0 @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5658]) ).
thf(5885,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( hAPP @ SX4 @ SX3 )
!= SX2 )
| ( ( c_Fun_Ofun__upd @ SX1 @ SX0 @ SX4 @ SX3 @ SX2 )
= SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5604]) ).
thf(5886,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX7 @ SX6 ) @ SX5 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX4 @ SX5 ) @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SX2 @ SX1 @ SX0 @ SX7 @ SX4 ) @ SX6 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5668]) ).
thf(5887,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX4 ) @ SX3 ) @ SX2 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX4 ) @ SX1 ) @ SX0 ) )
| ~ ( ( SX3 != SX1 )
| ( SX2 != SX0 ) ) )
| ~ ( ~ ~ ( ( SX3 != SX1 )
| ( SX2 != SX0 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX4 ) @ SX3 ) @ SX2 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX4 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5682]) ).
thf(5888,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5612]) ).
thf(5889,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SX0 ) @ SX1 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5614]) ).
thf(5890,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5564]) ).
thf(5891,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5580]) ).
thf(5892,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX3 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX3 ) @ SX0 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5590]) ).
thf(5893,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX2 != SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5509]) ).
thf(5894,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( SX2
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX1 ) @ SX0 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5684]) ).
thf(5895,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Orderings_Obot @ SX1 )
| ( class_Orderings_Obot @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5719]) ).
thf(5896,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5584]) ).
thf(5897,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SX2 @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX0 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5707]) ).
thf(5898,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Oorder @ SX2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX0 ) @ SX1 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5517]) ).
thf(5899,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) @ SX0 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) ) )
| ( SX0
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SX0
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) @ SX0 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5531]) ).
thf(5900,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX0 ) ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5565]) ).
thf(5901,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SX3 @ SX2 @ SX1 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SX3 @ SX0 @ SX2 )
| ( c_Hoare__Mirabelle_Ohoare__derivs @ SX3 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5500]) ).
thf(5902,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ! [SX3: $i] : ( hBOOL @ ( hAPP @ SX2 @ SX3 ) )
| ! [SX3: $i,SX4: $i] : ( hBOOL @ ( hAPP @ SX2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SX1 @ SX0 ) @ SX3 ) @ SX4 ) ) ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] : ( hBOOL @ ( hAPP @ SX2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SX1 @ SX0 ) @ SX3 ) @ SX4 ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5645]) ).
thf(5903,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Oorder @ SX2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX0 ) @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5522]) ).
thf(5904,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX5 @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) ) @ SX3 ) @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5635]) ).
thf(5905,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ SX1 ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5541]) ).
thf(5906,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Orderings_Opreorder @ SX1 )
| ( class_Orderings_Opreorder @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5713]) ).
thf(5907,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Opreorder @ SX2 )
| ( SX1 != SX0 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5523]) ).
thf(5908,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX5 @ SX4 ) @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) ) @ SX5 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX4 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5640]) ).
thf(5909,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SX4 @ SX3 @ SX2 )
| ( ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX0 ) )
= ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5620]) ).
thf(5910,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX2 ) @ SX1 ) @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[5683]) ).
thf(5911,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SX1 )
| ( class_Lattices_Obounded__lattice @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5709]) ).
thf(5912,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5593]) ).
thf(5913,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Orderings_Oorder @ SX3 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX2 ) @ SX1 ) )
| ( SX2 != SX0 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5518]) ).
thf(5914,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5613]) ).
thf(5915,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX3 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5599]) ).
thf(5916,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX2 ) @ SX1 ) @ SX0 ) )
| ( SX2 = SX0 )
| ( hBOOL @ ( hAPP @ SX1 @ SX0 ) ) )
| ~ ( ~ ( ( SX2 = SX0 )
| ( hBOOL @ ( hAPP @ SX1 @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5573]) ).
thf(5917,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX3 ) @ SX2 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX1 ) @ SX0 ) )
| ~ ! [SX5: $i] :
~ ( ~ ( ( SX3
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX1 ) @ SX5 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX5 ) @ SX2 )
!= SX0 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX3 ) @ SX5 )
!= SX1 )
| ( SX2
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX5 ) @ SX0 ) ) ) ) )
| ~ ( ~ ~ ! [SX5: $i] :
~ ( ~ ( ( SX3
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX1 ) @ SX5 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX5 ) @ SX2 )
!= SX0 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX3 ) @ SX5 )
!= SX1 )
| ( SX2
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX5 ) @ SX0 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX3 ) @ SX2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5688]) ).
thf(5918,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( class_Finite__Set_Ofinite @ SX1 )
| ~ ( class_Finite__Set_Ofinite @ SX0 ) )
| ( class_Finite__Set_Ofinite @ ( tc_fun @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5714]) ).
thf(5919,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5701]) ).
thf(5920,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX2 != SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) @ SX1 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5510]) ).
thf(5921,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SX3 @ SX2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5656]) ).
thf(5922,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ SX1 )
| ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5712]) ).
thf(5923,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SX3 @ SX2 @ SX1 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SX3 ) @ tc_HOL_Obool ) ) @ SX0 ) @ SX1 ) )
| ( c_Hoare__Mirabelle_Ohoare__derivs @ SX3 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5499]) ).
thf(5924,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SX2 ) @ SX1 )
!= SX0 )
| ( SX1
= ( hAPP @ ( c_List_Orev @ SX2 ) @ SX0 ) ) )
| ~ ( ( SX1
!= ( hAPP @ ( c_List_Orev @ SX2 ) @ SX0 ) )
| ( ( hAPP @ ( c_List_Orev @ SX2 ) @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5696]) ).
thf(5925,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SX4 @ SX3 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5655]) ).
thf(5926,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ! [SX7: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX7 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX7 ) @ SX0 ) ) ) )
| ~ ( ~ ~ ! [SX7: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX7 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX7 ) @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5670]) ).
thf(5927,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 )
| ( ( hAPP @ ( hAPP @ SX4 @ SX0 ) @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5621]) ).
thf(5928,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX5 @ SX4 ) @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX2 @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) ) @ SX5 ) @ SX0 ) @ SX4 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5642]) ).
thf(5929,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5601]) ).
thf(5930,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Orderings_Oorder @ SX3 )
| ( SX2 != SX1 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX0 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5520]) ).
thf(5931,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Oorder @ SX2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX0 ) @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5515]) ).
thf(5932,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Orderings_Oorder @ SX1 )
| ( class_Orderings_Oorder @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5716]) ).
thf(5933,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX5 @ SX4 ) @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX2 @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) ) @ SX0 ) @ SX5 ) @ SX4 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5641]) ).
thf(5934,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SX2 @ SX0 ) )
| ( hBOOL @ ( hAPP @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5542]) ).
thf(5935,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ( c_Typedef_Otype__definition @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 )
| ~ ( ~ ( ( ( hAPP @ SX4 @ SX1 )
!= ( hAPP @ SX4 @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( hAPP @ SX4 @ SX1 )
= ( hAPP @ SX4 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5660]) ).
thf(5936,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SX2 @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5545]) ).
thf(5937,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Predicate_Oreflp @ SX2 @ SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5665]) ).
thf(5938,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( c_Typedef_Otype__definition @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 )
| ( ( hAPP @ SX2 @ ( hAPP @ SX3 @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5659]) ).
thf(5939,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SX1 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX1 @ ( c_Hilbert__Choice_OEps @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5678]) ).
thf(5940,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5577]) ).
thf(5941,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) @ SX1 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5501]) ).
thf(5942,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Wellfounded_OwfP @ SX2 @ SX1 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) @ SX0 ) @ SX1 ) )
| ( c_Wellfounded_OwfP @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5674]) ).
thf(5943,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Oorder @ SX2 )
| ~ ( ~ ( ( SX1 != SX0 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX0 ) @ SX1 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX0 ) @ SX1 ) ) )
| ( SX1 = SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5524]) ).
thf(5944,plain,
( ( ! [SX0: $i] :
( ( hAPP @ c_Nat_OSuc @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[5617]) ).
thf(5945,plain,
! [SV1: $i] :
( ( ! [SY917: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY917 @ tc_HOL_Obool ) ) @ SV1 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5506]) ).
thf(5946,plain,
! [SV2: $i] :
( ( ! [SY918: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY918 @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY918 @ tc_HOL_Obool ) ) ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5529]) ).
thf(5947,plain,
! [SV3: $i] :
( ( ! [SY919: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY919 @ tc_HOL_Obool ) ) @ SV3 ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY919 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5530]) ).
thf(5948,plain,
! [SV4: $i] :
( ( ! [SY920: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ SY920 @ SV4 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY920 ) @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5532]) ).
thf(5949,plain,
! [SV5: $i] :
( ( ! [SY921: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ SY921 @ SV5 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY921 ) @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5533]) ).
thf(5950,plain,
! [SV6: $i] :
( ( ! [SY922: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY922 @ tc_HOL_Obool ) ) @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5536]) ).
thf(5951,plain,
! [SV7: $i] :
( ( ! [SY923: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY923 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY923 @ tc_HOL_Obool ) ) @ SV7 ) )
= SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5538]) ).
thf(5952,plain,
! [SV8: $i] :
( ( ! [SY924: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY924 @ tc_HOL_Obool ) ) @ SV8 ) @ SV8 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5546]) ).
thf(5953,plain,
! [SV9: $i] :
( ( ! [SY925: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY925 @ tc_HOL_Obool ) ) @ SV9 ) @ SV9 )
= SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5547]) ).
thf(5954,plain,
! [SV10: $i] :
( ( ! [SY926: $i,SY927: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY927 @ tc_HOL_Obool ) ) @ SY926 ) @ SV10 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY927 @ tc_HOL_Obool ) ) @ SV10 ) @ SY926 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5548]) ).
thf(5955,plain,
! [SV11: $i] :
( ( ! [SY928: $i,SY929: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY929 @ tc_HOL_Obool ) ) @ SY928 ) @ SV11 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY929 @ tc_HOL_Obool ) ) @ SV11 ) @ SY928 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5549]) ).
thf(5956,plain,
! [SV12: $i] :
( ( ! [SY930: $i,SY931: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY931 @ tc_HOL_Obool ) ) @ SY930 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY931 @ tc_HOL_Obool ) ) @ SY930 ) @ SV12 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY931 @ tc_HOL_Obool ) ) @ SY930 ) @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5550]) ).
thf(5957,plain,
! [SV13: $i] :
( ( ! [SY932: $i,SY933: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY933 @ tc_HOL_Obool ) ) @ SY932 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY933 @ tc_HOL_Obool ) ) @ SY932 ) @ SV13 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY933 @ tc_HOL_Obool ) ) @ SY932 ) @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5551]) ).
thf(5958,plain,
! [SV14: $i] :
( ( ! [SY934: $i,SY935: $i,SY936: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY936 @ tc_HOL_Obool ) ) @ SY935 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY936 @ tc_HOL_Obool ) ) @ SY934 ) @ SV14 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY936 @ tc_HOL_Obool ) ) @ SY934 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY936 @ tc_HOL_Obool ) ) @ SY935 ) @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5552]) ).
thf(5959,plain,
! [SV15: $i] :
( ( ! [SY937: $i,SY938: $i,SY939: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY939 @ tc_HOL_Obool ) ) @ SY938 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY939 @ tc_HOL_Obool ) ) @ SY937 ) @ SV15 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY939 @ tc_HOL_Obool ) ) @ SY937 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY939 @ tc_HOL_Obool ) ) @ SY938 ) @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5553]) ).
thf(5960,plain,
! [SV16: $i] :
( ( ! [SY940: $i,SY941: $i,SY942: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY942 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY942 @ tc_HOL_Obool ) ) @ SY941 ) @ SY940 ) ) @ SV16 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY942 @ tc_HOL_Obool ) ) @ SY941 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY942 @ tc_HOL_Obool ) ) @ SY940 ) @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5554]) ).
thf(5961,plain,
! [SV17: $i] :
( ( ! [SY943: $i,SY944: $i,SY945: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY945 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY945 @ tc_HOL_Obool ) ) @ SY944 ) @ SY943 ) ) @ SV17 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY945 @ tc_HOL_Obool ) ) @ SY944 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY945 @ tc_HOL_Obool ) ) @ SY943 ) @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5555]) ).
thf(5962,plain,
! [SV18: $i] :
( ( ! [SY946: $i,SY947: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY947 @ tc_HOL_Obool ) ) @ SY946 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY947 @ tc_HOL_Obool ) ) @ SY946 ) @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5560]) ).
thf(5963,plain,
! [SV19: $i] :
( ( ! [SY948: $i,SY949: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY949 @ tc_HOL_Obool ) ) @ SY948 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY949 @ tc_HOL_Obool ) ) @ SV19 ) @ SY948 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5561]) ).
thf(5964,plain,
! [SV20: $i] :
( ( ! [SY950: $i,SY951: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY951 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY951 @ tc_HOL_Obool ) ) @ SY950 ) @ SV20 ) ) @ SY950 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5567]) ).
thf(5965,plain,
! [SV21: $i] :
( ( ! [SY952: $i,SY953: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY953 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY953 @ tc_HOL_Obool ) ) @ SY952 ) @ SV21 ) ) @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5568]) ).
thf(5966,plain,
! [SV22: $i] :
( ( ! [SY954: $i,SY955: $i,SY956: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY956 ) @ SY955 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY956 ) @ SY954 ) @ SV22 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY956 ) @ SY954 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY956 ) @ SY955 ) @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5574]) ).
thf(5967,plain,
! [SV23: $i] :
( ( ! [SY957: $i,SY958: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY958 ) @ SY957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY958 ) @ SY957 ) @ SV23 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY958 ) @ SY957 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5575]) ).
thf(5968,plain,
! [SV24: $i] :
( ( ! [SY959: $i,SY960: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY960 @ tc_HOL_Obool ) ) @ SY959 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY960 ) @ SV24 ) @ SY959 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5578]) ).
thf(5969,plain,
! [SV25: $i] :
( ( ! [SY961: $i,SY962: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY962 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY962 @ tc_HOL_Obool ) ) @ SY961 ) @ SV25 ) ) @ SV25 )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY962 @ tc_HOL_Obool ) ) @ SY961 ) @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5587]) ).
thf(5970,plain,
! [SV26: $i] :
( ( ! [SY963: $i,SY964: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY964 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY964 @ tc_HOL_Obool ) ) @ SY963 ) @ SV26 ) ) @ SY963 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5589]) ).
thf(5971,plain,
! [SV27: $i] :
( ( ! [SY965: $i,SY966: $i,SY967: $i] :
( ( c_Fun_Ofun__upd @ SY967 @ SY966 @ SY965 @ SV27 @ ( hAPP @ SY965 @ SV27 ) )
= SY965 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5603]) ).
thf(5972,plain,
! [SV28: $i] :
( ( ! [SY968: $i,SY969: $i,SY970: $i,SY971: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SY971 @ SY970 @ SY969 @ SY968 @ SV28 ) @ SY968 )
= SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5607]) ).
thf(5973,plain,
! [SV29: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV29 ) @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5610]) ).
thf(5974,plain,
! [SV30: $i] :
( ( ! [SY972: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SY972 ) @ SV30 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV30 ) @ SY972 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5611]) ).
thf(5975,plain,
! [SV31: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV31 ) @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5622]) ).
thf(5976,plain,
! [SV32: $i] :
( ( ! [SY973: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SY973 ) @ SV32 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV32 ) @ SY973 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5623]) ).
thf(5977,plain,
! [SV33: $i] :
( ( ! [SY974: $i,SY975: $i,SY976: $i,SY977: $i,SY978: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY978 @ SY977 @ SY976 @ SY975 ) @ SY974 ) @ SV33 )
= ( hAPP @ SY975 @ ( hAPP @ SY974 @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5630]) ).
thf(5978,plain,
! [SV34: $i] :
( ( ! [SY979: $i,SY980: $i,SY981: $i,SY982: $i,SY983: $i,SY984: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY984 @ SY983 @ SY982 @ SY981 ) @ ( hAPP @ ( c_Fun_Ocomp @ SY980 @ SY984 @ SY982 @ SY979 ) @ SV34 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SY980 @ SY983 @ SY982 @ ( hAPP @ ( c_Fun_Ocomp @ SY984 @ SY983 @ SY980 @ SY981 ) @ SY979 ) ) @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5631]) ).
thf(5979,plain,
! [SV35: $i] :
( ( ! [SY985: $i,SY986: $i,SY987: $i,SY988: $i,SY989: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY989 @ SY988 @ SY987 @ SY986 ) @ SY985 ) @ SV35 )
= ( hAPP @ SY986 @ ( hAPP @ SY985 @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5632]) ).
thf(5980,plain,
! [SV36: $i] :
( ( ! [SY990: $i,SY991: $i,SY992: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY992 @ ( tc_fun @ SY991 @ tc_HOL_Obool ) ) ) @ SY990 ) @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5638]) ).
thf(5981,plain,
! [SV37: $i] :
( ( ! [SY993: $i] :
( ( hAPP @ ( c_Set_OCollect @ SY993 ) @ SV37 )
= SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5663]) ).
thf(5982,plain,
! [SV38: $i] :
( ( ! [SY994: $i] :
( ( hAPP @ ( c_Fun_Oid @ SY994 ) @ SV38 )
= SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5664]) ).
thf(5983,plain,
! [SV39: $i] :
( ( ! [SY995: $i] :
( ( hAPP @ ( c_Fun_Oid @ SY995 ) @ SV39 )
= SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5666]) ).
thf(5984,plain,
! [SV40: $i] :
( ( ! [SY996: $i,SY997: $i,SY998: $i,SY999: $i,SY1000: $i,SY1001: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1001 @ SY1000 @ SY999 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1001 @ SY998 @ SY1000 ) @ SY997 ) @ SY996 ) ) @ SV40 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1001 @ SY998 @ SY999 ) @ SY997 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY998 @ SY1000 @ SY999 ) @ SY996 ) @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5667]) ).
thf(5985,plain,
! [SV41: $i] :
( ( ! [SY1002: $i,SY1003: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SY1003 @ SY1002 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY1002 @ SY1003 ) @ SV41 ) )
= SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5680]) ).
thf(5986,plain,
! [SV42: $i] :
( ( ! [SY1004: $i,SY1005: $i,SY1006: $i] :
( ( hAPP @ SY1006 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY1005 @ SY1005 ) @ SY1004 ) @ SY1006 ) @ SV42 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY1005 @ SY1005 ) @ SY1004 ) @ SY1006 ) @ ( hAPP @ SY1006 @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5681]) ).
thf(5987,plain,
! [SV43: $i] :
( ( ! [SY1007: $i,SY1008: $i,SY1009: $i,SY1010: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1010 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1010 @ SY1009 ) @ SY1008 ) @ SY1007 ) ) @ SY1008 ) @ SV43 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1010 @ SY1009 ) @ SY1008 ) @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5686]) ).
thf(5988,plain,
! [SV44: $i] :
( ( ! [SY1011: $i,SY1012: $i,SY1013: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1013 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1013 ) @ SY1012 ) @ SY1011 ) ) @ SV44 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1013 ) @ SY1012 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1013 ) @ SY1011 ) @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5687]) ).
thf(5989,plain,
! [SV45: $i] :
( ( ! [SY1014: $i] :
( ( hAPP @ ( c_List_Orev @ SY1014 ) @ ( hAPP @ ( c_List_Orev @ SY1014 ) @ SV45 ) )
= SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5697]) ).
thf(5990,plain,
! [SV46: $i] :
( ( class_Nat_Osize @ ( tc_Hoare__Mirabelle_Otriple @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5741]) ).
thf(5991,plain,
! [SV47: $i] :
( ( ! [SY1015: $i] :
( ( hAPP @ ( c_COMBI @ SY1015 ) @ SV47 )
= SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5742]) ).
thf(5992,plain,
! [SV48: $i] :
( ( ! [SY1016: $i,SY1017: $i,SY1018: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ SY1018 @ SY1017 ) @ SY1016 ) @ SV48 )
= SY1016 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5743]) ).
thf(5993,plain,
! [SV49: $i] :
( ( ! [SY1019: $i,SY1020: $i,SY1021: $i,SY1022: $i,SY1023: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1023 @ SY1022 @ SY1021 ) @ SY1020 ) @ SY1019 ) @ SV49 )
= ( hAPP @ SY1020 @ ( hAPP @ SY1019 @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5744]) ).
thf(5994,plain,
! [SV50: $i] :
( ( ! [SY1024: $i,SY1025: $i,SY1026: $i,SY1027: $i,SY1028: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1028 @ SY1027 @ SY1026 ) @ SY1025 ) @ SY1024 ) @ SV50 )
= ( hAPP @ ( hAPP @ SY1025 @ SV50 ) @ SY1024 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5745]) ).
thf(5995,plain,
! [SV51: $i] :
( ( ! [SY1029: $i,SY1030: $i,SY1031: $i,SY1032: $i,SY1033: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1033 @ SY1032 @ SY1031 ) @ SY1030 ) @ SY1029 ) @ SV51 )
= ( hAPP @ ( hAPP @ SY1030 @ SV51 ) @ ( hAPP @ SY1029 @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5746]) ).
thf(5996,plain,
! [SV52: $i] :
( ( ! [SY1034: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SY1034 ) @ SV52 ) )
| ( SY1034 = SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5747]) ).
thf(5997,plain,
( ( hBOOL @ c_fFalse )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5749]) ).
thf(5998,plain,
! [SV53: $i] :
( ( ~ ( hBOOL @ ( hAPP @ c_fNot @ SV53 ) )
| ~ ( hBOOL @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5751]) ).
thf(5999,plain,
! [SV54: $i] :
( ( ~ ~ ( hBOOL @ SV54 )
| ( hBOOL @ ( hAPP @ c_fNot @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5752]) ).
thf(6000,plain,
! [SV55: $i] :
( ( ! [SY1035: $i] :
( ~ ( hBOOL @ SY1035 )
| ~ ( hBOOL @ SV55 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SY1035 ) @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5753]) ).
thf(6001,plain,
! [SV56: $i] :
( ( ! [SY1036: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SY1036 ) @ SV56 ) )
| ( hBOOL @ SY1036 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5754]) ).
thf(6002,plain,
! [SV57: $i] :
( ( ! [SY1037: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SY1037 ) @ SV57 ) )
| ( hBOOL @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5755]) ).
thf(6003,plain,
! [SV58: $i] :
( ( ! [SY1038: $i] :
( ~ ( hBOOL @ SY1038 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SY1038 ) @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5756]) ).
thf(6004,plain,
! [SV59: $i] :
( ( ! [SY1039: $i] :
( ~ ( hBOOL @ SY1039 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV59 ) @ SY1039 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5757]) ).
thf(6005,plain,
! [SV60: $i] :
( ( ! [SY1040: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SY1040 ) @ SV60 ) )
| ( hBOOL @ SY1040 )
| ( hBOOL @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5758]) ).
thf(6006,plain,
! [SV61: $i] :
( ( ! [SY1041: $i] :
( ( hBOOL @ SY1041 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SY1041 ) @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5759]) ).
thf(6007,plain,
! [SV62: $i] :
( ( ! [SY1042: $i] :
( ~ ( hBOOL @ SY1042 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV62 ) @ SY1042 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5760]) ).
thf(6008,plain,
! [SV63: $i] :
( ( ! [SY1043: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SY1043 ) @ SV63 ) )
| ~ ( hBOOL @ SY1043 )
| ( hBOOL @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5761]) ).
thf(6009,plain,
( ( c_Hoare__Mirabelle_Ohoare__derivs @ t_a @ sK1_B_G @ v_ts )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5763]) ).
thf(6010,plain,
! [SV64: $i] :
( ( ! [SY1044: $i,SY1045: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1045 @ tc_HOL_Obool ) ) @ SY1044 ) @ SV64 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1045 @ tc_HOL_Obool ) ) @ SV64 ) @ SY1044 )
= SY1044 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5764]) ).
thf(6011,plain,
! [SV65: $i] :
( ( ! [SY1046: $i,SY1047: $i,SY1048: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1048 @ SY1047 ) )
| ~ ( hBOOL @ ( hAPP @ SY1046 @ SY1047 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV65 @ tc_HOL_Obool ) ) @ SY1048 ) @ SY1046 ) @ SY1047 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5765]) ).
thf(6012,plain,
! [SV66: $i] :
( ( ! [SY1049: $i,SY1050: $i,SY1051: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1051 @ tc_HOL_Obool ) ) @ SY1050 ) @ SY1049 ) @ SV66 ) )
| ( hBOOL @ ( hAPP @ SY1050 @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5766]) ).
thf(6013,plain,
! [SV67: $i] :
( ( ! [SY1052: $i,SY1053: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1053 @ tc_HOL_Obool ) ) @ SY1052 ) @ SV67 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1053 @ tc_HOL_Obool ) ) @ SY1052 ) @ SV67 )
= SV67 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1053 @ tc_HOL_Obool ) ) @ SY1052 ) @ SV67 )
!= SV67 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1053 @ tc_HOL_Obool ) ) @ SY1052 ) @ SV67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5767]) ).
thf(6014,plain,
! [SV68: $i] :
( ( ! [SY1054: $i,SY1055: $i] :
( ~ ( class_Orderings_Olinorder @ SY1055 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1055 ) @ SY1054 ) @ SV68 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1055 ) @ SV68 ) @ SY1054 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5768]) ).
thf(6015,plain,
! [SV69: $i] :
( ( ! [SY1056: $i,SY1057: $i,SY1058: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1058 @ SY1057 @ SY1056 ) @ SV69 ) )
| ~ ! [SY1059: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1056 @ SY1059 ) @ SV69 ) ) )
| ~ ( ~ ~ ! [SY1060: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1056 @ SY1060 ) @ SV69 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1058 @ SY1057 @ SY1056 ) @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5769]) ).
thf(6016,plain,
! [SV70: $i] :
( ( ! [SY1061: $i] :
~ ( ~ ( ~ ( c_Equiv__Relations_Opart__equivp @ SY1061 @ SV70 )
| ~ ( ~ ~ ! [SY1062: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1062 ) @ SY1062 ) )
| ~ ! [SY1063: $i,SY1064: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1064 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1064 ) @ SY1064 ) ) )
| ( ( hAPP @ SV70 @ SY1063 )
!= ( hAPP @ SV70 @ SY1064 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1064 ) @ SY1064 ) ) )
| ( ( hAPP @ SV70 @ SY1063 )
!= ( hAPP @ SV70 @ SY1064 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1064 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ! [SY1065: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1065 ) @ SY1065 ) )
| ~ ! [SY1066: $i,SY1067: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) ) ) ) )
| ( c_Equiv__Relations_Opart__equivp @ SY1061 @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5770]) ).
thf(6017,plain,
! [SV71: $i] :
( ( ! [SY1068: $i,SY1069: $i,SY1070: $i] :
( ( SY1070 != SY1069 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1068 ) @ SV71 ) @ SY1070 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1068 ) @ SV71 ) @ SY1069 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1068 ) @ SV71 ) @ SY1069 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1068 ) @ SV71 ) @ SY1070 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5771]) ).
thf(6018,plain,
! [SV72: $i] :
( ( ! [SY1071: $i] :
( ~ ( class_Orderings_Otop @ SY1071 )
| ( class_Orderings_Otop @ ( tc_fun @ SV72 @ SY1071 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5772]) ).
thf(6019,plain,
! [SV73: $i] :
( ( ! [SY1072: $i,SY1073: $i,SY1074: $i,SY1075: $i,SY1076: $i,SY1077: $i,SY1078: $i,SY1079: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1079 @ SY1078 @ SY1077 @ SY1076 ) @ SY1075 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY1074 @ SY1078 @ SY1077 @ SY1073 ) @ SY1072 ) )
| ( ( hAPP @ SY1076 @ ( hAPP @ SY1075 @ SV73 ) )
= ( hAPP @ SY1073 @ ( hAPP @ SY1072 @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5773]) ).
thf(6020,plain,
! [SV74: $i] :
( ( ! [SY1080: $i,SY1081: $i,SY1082: $i] :
( ~ ( class_Orderings_Oord @ SY1082 )
| ~ ! [SX4: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1082 ) @ ( hAPP @ SY1081 @ SX4 ) ) @ ( hAPP @ SY1080 @ SX4 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV74 @ SY1082 ) ) @ SY1081 ) @ SY1080 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5774]) ).
thf(6021,plain,
! [SV75: $i] :
( ( ! [SY1084: $i,SY1085: $i,SY1086: $i,SY1087: $i,SY1088: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1088 @ SY1087 ) @ SY1086 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1085 @ SY1087 ) @ SY1086 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1084 @ ( tc_fun @ SV75 @ tc_HOL_Obool ) ) ) @ SY1088 ) @ SY1085 ) @ SY1087 ) @ SY1086 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5775]) ).
thf(6022,plain,
! [SV76: $i] :
( ( SV76
!= ( hAPP @ c_Nat_OSuc @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5776]) ).
thf(6023,plain,
! [SV77: $i] :
( ( ! [SY1089: $i,SY1090: $i] :
( ( SY1090 != SY1089 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV77 @ tc_HOL_Obool ) ) @ SY1090 ) @ SY1089 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV77 @ tc_HOL_Obool ) ) @ SY1089 ) @ SY1090 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5777]) ).
thf(6024,plain,
! [SV78: $i] :
( ( ! [SY1091: $i,SY1092: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1092 @ tc_HOL_Obool ) ) @ SY1091 ) @ SV78 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SY1092 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ SY1092 @ SY1091 ) ) @ ( c_Predicate_OPowp @ SY1092 @ SV78 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5778]) ).
thf(6025,plain,
! [SV79: $i] :
( ( ! [SY1093: $i] :
( ( SY1093 != SV79 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SY1093 ) @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5779]) ).
thf(6026,plain,
! [SV80: $i] :
( ( ! [SY1094: $i,SY1095: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY1095 @ SY1094 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1094 @ SV80 ) @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5780]) ).
thf(6027,plain,
! [SV81: $i] :
( ( ! [SY1096: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SY1096 )
| ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV81 @ SY1096 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5781]) ).
thf(6028,plain,
! [SV82: $i] :
( ( ! [SY1097: $i,SY1098: $i,SY1099: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SY1099 @ SY1098 @ SY1097 )
| ( ( hAPP @ ( hAPP @ SY1098 @ SV82 ) @ SV82 )
= SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5782]) ).
thf(6029,plain,
! [SV83: $i] :
( ( ! [SY1100: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SY1100 )
!= ( hAPP @ c_Nat_OSuc @ SV83 ) )
| ( SY1100 = SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5783]) ).
thf(6030,plain,
! [SV84: $i] :
( ( ! [SY1101: $i,SY1102: $i,SY1103: $i,SY1104: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1104 @ tc_HOL_Obool ) ) @ SY1103 ) @ SY1102 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1101 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ SY1101 @ SY1104 @ SV84 ) @ SY1103 ) ) @ ( hAPP @ ( c_Set_Ovimage @ SY1101 @ SY1104 @ SV84 ) @ SY1102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5784]) ).
thf(6031,plain,
! [SV85: $i] :
( ( ! [SY1105: $i,SY1106: $i] :
( ~ ~ ! [SX3: $i] :
~ ( hBOOL @ ( hAPP @ SY1106 @ SX3 ) )
| ( SY1105
!= ( c_Hilbert__Choice_OEps @ SV85 @ SY1106 ) )
| ( hBOOL @ ( hAPP @ SY1106 @ SY1105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5785]) ).
thf(6032,plain,
! [SV86: $i] :
( ( ! [SY1108: $i,SY1109: $i,SY1110: $i] :
( ( SY1110 != SY1109 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1108 ) @ SV86 ) @ SY1110 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1108 ) @ SV86 ) @ SY1109 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1108 ) @ SV86 ) @ SY1110 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1108 ) @ SV86 ) @ SY1109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5786]) ).
thf(6033,plain,
! [SV87: $i] :
( ( ! [SY1111: $i,SY1112: $i,SY1113: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1113 @ tc_HOL_Obool ) ) @ SY1112 ) @ SY1111 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1113 @ tc_HOL_Obool ) ) @ SY1111 ) @ SV87 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1113 @ tc_HOL_Obool ) ) @ SY1112 ) @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5787]) ).
thf(6034,plain,
! [SV88: $i] :
( ( ! [SY1114: $i,SY1115: $i,SY1116: $i,SY1117: $i,SY1118: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1118 @ ( tc_fun @ SY1117 @ tc_HOL_Obool ) ) ) @ SY1116 ) @ SY1115 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1116 @ SY1114 ) @ SV88 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1115 @ SY1114 ) @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5788]) ).
thf(6035,plain,
! [SV89: $i] :
( ( ! [SY1119: $i] :
~ ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SY1119 )
!= ( hAPP @ c_Int_ORep__Integ @ SV89 ) )
| ( SY1119 = SV89 ) )
| ~ ( ( SY1119 != SV89 )
| ( ( hAPP @ c_Int_ORep__Integ @ SY1119 )
= ( hAPP @ c_Int_ORep__Integ @ SV89 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5789]) ).
thf(6036,plain,
! [SV90: $i] :
( ( ! [SY1120: $i,SY1121: $i,SY1122: $i,SY1123: $i,SY1124: $i] :
( ~ ( ( SY1124 != SY1123 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1122 @ SY1121 @ SY1120 @ SY1123 @ SV90 ) @ SY1124 )
= ( hAPP @ SY1120 @ SY1124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5790]) ).
thf(6037,plain,
! [SV91: $i] :
( ( ! [SY1125: $i,SY1126: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY1126 ) @ SY1125 )
!= ( hAPP @ ( c_List_Orev @ SY1126 ) @ SV91 ) )
| ( SY1125 = SV91 ) )
| ~ ( ( SY1125 != SV91 )
| ( ( hAPP @ ( c_List_Orev @ SY1126 ) @ SY1125 )
= ( hAPP @ ( c_List_Orev @ SY1126 ) @ SV91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5791]) ).
thf(6038,plain,
! [SV92: $i] :
( ( ! [SY1127: $i,SY1128: $i,SY1129: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1129 @ SY1128 @ SY1127 ) @ SV92 ) )
| ~ ! [SY1130: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1127 @ SV92 ) @ SY1130 ) ) )
| ~ ( ~ ~ ! [SY1131: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1127 @ SV92 ) @ SY1131 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1129 @ SY1128 @ SY1127 ) @ SV92 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5792]) ).
thf(6039,plain,
! [SV93: $i] :
( ( ! [SY1132: $i,SY1133: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1133 ) @ tc_HOL_Obool ) ) @ SY1132 ) @ SV93 ) )
| ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1133 @ SV93 @ SY1132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5793]) ).
thf(6040,plain,
! [SV94: $i] :
( ( ! [SY1134: $i] :
( ~ ( class_Groups_Ouminus @ SY1134 )
| ( class_Groups_Ouminus @ ( tc_fun @ SV94 @ SY1134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5794]) ).
thf(6041,plain,
! [SV95: $i] :
( ( ! [SY1135: $i,SY1136: $i,SY1137: $i,SY1138: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1138 @ tc_HOL_Obool ) ) @ SY1137 ) @ SY1136 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1138 @ tc_HOL_Obool ) ) @ SY1135 ) @ SV95 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1138 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1138 @ tc_HOL_Obool ) ) @ SY1137 ) @ SY1135 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1138 @ tc_HOL_Obool ) ) @ SY1136 ) @ SV95 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5795]) ).
thf(6042,plain,
! [SV96: $i] :
( ( ! [SY1139: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SY1139 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV96 ) )
| ( SY1139 = SV96 ) )
| ~ ( ( SY1139 != SV96 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SY1139 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV96 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5796]) ).
thf(6043,plain,
! [SV97: $i] :
( ( ! [SY1140: $i,SY1141: $i,SY1142: $i,SY1143: $i,SY1144: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1144 @ ( tc_fun @ SY1143 @ tc_HOL_Obool ) ) ) @ SY1142 ) @ SY1141 ) @ SY1140 ) @ SV97 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1142 @ SY1140 ) @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5797]) ).
thf(6044,plain,
! [SV98: $i] :
( ( ! [SY1145: $i,SY1146: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1146 @ tc_HOL_Obool ) ) @ SY1145 ) @ SV98 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1146 @ tc_HOL_Obool ) ) @ SY1145 ) @ SV98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5798]) ).
thf(6045,plain,
! [SV99: $i] :
( ( ! [SY1147: $i,SY1148: $i,SY1149: $i,SY1150: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1150 @ SY1149 @ SY1148 ) @ SY1147 ) @ SV99 ) )
| ( hBOOL @ ( hAPP @ SY1147 @ ( hAPP @ SY1148 @ SV99 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY1147 @ ( hAPP @ SY1148 @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1150 @ SY1149 @ SY1148 ) @ SY1147 ) @ SV99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5799]) ).
thf(6046,plain,
! [SV100: $i] :
( ( ! [SY1151: $i,SY1152: $i,SY1153: $i,SY1154: $i,SY1155: $i,SY1156: $i,SY1157: $i,SY1158: $i,SY1159: $i,SY1160: $i] :
( ( ( hAPP @ SY1160 @ ( hAPP @ SY1159 @ SY1158 ) )
!= ( hAPP @ SY1157 @ ( hAPP @ SY1156 @ SY1155 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1154 @ SY1153 @ SY1152 @ SY1160 ) @ SY1159 ) @ SY1158 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1151 @ SY1153 @ SV100 @ SY1157 ) @ SY1156 ) @ SY1155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5800]) ).
thf(6047,plain,
! [SV101: $i] :
( ( ! [SY1161: $i,SY1162: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1162 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1162 @ tc_HOL_Obool ) ) @ SY1161 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1162 @ tc_HOL_Obool ) ) @ SV101 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1162 @ tc_HOL_Obool ) ) @ SV101 ) @ SY1161 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1162 @ tc_HOL_Obool ) ) @ SV101 ) @ SY1161 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1162 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1162 @ tc_HOL_Obool ) ) @ SY1161 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1162 @ tc_HOL_Obool ) ) @ SV101 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5801]) ).
thf(6048,plain,
! [SV102: $i] :
( ( ! [SY1163: $i,SY1164: $i,SY1165: $i,SY1166: $i,SY1167: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY1167 @ SY1166 @ SY1165 )
| ( ( hAPP @ ( hAPP @ SY1165 @ SY1164 ) @ ( hAPP @ ( hAPP @ SY1165 @ SY1163 ) @ SV102 ) )
= ( hAPP @ ( hAPP @ SY1165 @ SY1163 ) @ ( hAPP @ ( hAPP @ SY1165 @ SY1164 ) @ SV102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5802]) ).
thf(6049,plain,
! [SV103: $i] :
( ( ! [SY1168: $i,SY1169: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1169 @ SY1168 ) @ SV103 ) )
| ! [SY1170: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1168 @ SY1170 ) @ SV103 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1169 @ SY1168 ) @ SY1170 ) ) ) )
| ~ ( ~ ! [SY1171: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1168 @ SY1171 ) @ SV103 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1169 @ SY1168 ) @ SY1171 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1169 @ SY1168 ) @ SV103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5803]) ).
thf(6050,plain,
! [SV104: $i] :
( ( ! [SY1172: $i,SY1173: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1173 @ tc_HOL_Obool ) ) @ SY1172 ) @ SV104 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1173 @ tc_HOL_Obool ) ) @ SY1172 ) @ SV104 )
= SY1172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5804]) ).
thf(6051,plain,
! [SV105: $i] :
( ( ! [SY1174: $i,SY1175: $i,SY1176: $i,SY1177: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SY1177 @ SY1176 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1176 @ SY1175 ) @ SY1174 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1176 @ SY1174 ) @ SV105 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1176 @ SY1175 ) @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5805]) ).
thf(6052,plain,
! [SV106: $i] :
( ( ! [SY1178: $i] :
( ~ ( class_Orderings_Opreorder @ SY1178 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1178 ) @ SV106 ) @ SV106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5806]) ).
thf(6053,plain,
! [SV107: $i] :
( ( ! [SY1179: $i] :
( ~ ( class_Lattices_Olattice @ SY1179 )
| ( class_Lattices_Olattice @ ( tc_fun @ SV107 @ SY1179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5807]) ).
thf(6054,plain,
! [SV108: $i] :
( ( ! [SY1180: $i] :
( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SY1180 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SY1180 @ ( c_Hilbert__Choice_OEps @ SV108 @ SY1180 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5808]) ).
thf(6055,plain,
! [SV109: $i] :
( ( ! [SY1182: $i,SY1183: $i,SY1184: $i,SY1185: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1185 @ SY1184 ) @ SY1183 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1182 @ SV109 @ SY1185 ) @ SY1183 ) @ SY1184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5809]) ).
thf(6056,plain,
! [SV110: $i] :
( ( ! [SY1186: $i,SY1187: $i,SY1188: $i,SY1189: $i] :
~ ( ~ ( ( ( c_Fun_Ofun__upd @ SY1189 @ SY1188 @ SY1187 @ SY1186 @ SV110 )
!= SY1187 )
| ( ( hAPP @ SY1187 @ SY1186 )
= SV110 ) )
| ~ ( ( ( hAPP @ SY1187 @ SY1186 )
!= SV110 )
| ( ( c_Fun_Ofun__upd @ SY1189 @ SY1188 @ SY1187 @ SY1186 @ SV110 )
= SY1187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5810]) ).
thf(6057,plain,
! [SV111: $i] :
( ( ! [SY1190: $i,SY1191: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1191 @ tc_HOL_Obool ) ) @ SY1190 ) @ SV111 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SY1191 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ SY1191 ) @ SY1190 ) ) @ ( hAPP @ ( c_Set_OPow @ SY1191 ) @ SV111 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5811]) ).
thf(6058,plain,
! [SV112: $i] :
( ( ! [SY1192: $i,SY1193: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1193 @ SY1192 ) @ SV112 ) )
| ! [SY1194: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1192 @ SY1194 ) @ SV112 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1193 @ SY1192 ) @ SY1194 ) ) ) )
| ~ ( ~ ! [SY1195: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1192 @ SY1195 ) @ SV112 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1193 @ SY1192 ) @ SY1195 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1193 @ SY1192 ) @ SV112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5812]) ).
thf(6059,plain,
! [SV113: $i] :
( ( ! [SY1196: $i,SY1197: $i,SY1198: $i] :
( ~ ( c_Predicate_Osymp @ SY1198 @ SY1197 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1197 @ SY1196 ) @ SV113 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1197 @ SV113 ) @ SY1196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5813]) ).
thf(6060,plain,
! [SV114: $i] :
( ( ! [SY1199: $i,SY1200: $i,SY1201: $i,SY1202: $i,SY1203: $i] :
~ ( ~ ( ( SY1203 != SY1202 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1201 @ SY1200 @ SY1199 @ SY1202 @ SV114 ) @ SY1203 )
= SV114 ) )
| ~ ( ~ ( ( SY1203 != SY1202 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1201 @ SY1200 @ SY1199 @ SY1202 @ SV114 ) @ SY1203 )
= ( hAPP @ SY1199 @ SY1203 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5814]) ).
thf(6061,plain,
! [SV115: $i] :
( ( ! [SY1204: $i,SY1205: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1205 @ tc_HOL_Obool ) ) @ SY1204 ) @ SV115 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY1205 ) @ SV115 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY1205 ) @ SY1204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5815]) ).
thf(6062,plain,
! [SV116: $i] :
( ( ! [SY1206: $i] :
( ~ ~ ( ~ ( class_Enum_Oenum @ SY1206 )
| ~ ( class_Enum_Oenum @ SV116 ) )
| ( class_Enum_Oenum @ ( tc_fun @ SY1206 @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5816]) ).
thf(6063,plain,
! [SV117: $i] :
( ( ! [SY1207: $i,SY1208: $i,SY1209: $i,SY1210: $i,SY1211: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1211 @ SY1210 ) @ SY1209 ) @ SY1208 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1211 @ SY1210 ) @ SY1207 ) @ SV117 ) )
| ~ ( ( SY1209 != SY1207 )
| ( SY1208 != SV117 ) ) )
| ~ ( ~ ~ ( ( SY1209 != SY1207 )
| ( SY1208 != SV117 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1211 @ SY1210 ) @ SY1209 ) @ SY1208 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1211 @ SY1210 ) @ SY1207 ) @ SV117 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5817]) ).
thf(6064,plain,
! [SV118: $i] :
( ( ! [SY1212: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SY1212 ) @ SV118 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV118 ) @ SY1212 ) )
| ( SY1212 = SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5818]) ).
thf(6065,plain,
! [SV119: $i] :
( ( ! [SY1213: $i,SY1214: $i,SY1215: $i,SY1216: $i,SY1217: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1217 @ ( tc_fun @ SY1216 @ tc_HOL_Obool ) ) ) @ SY1215 ) @ SY1214 ) @ SY1213 ) @ SV119 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1214 @ SY1213 ) @ SV119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5819]) ).
thf(6066,plain,
! [SV120: $i] :
( ( ! [SY1218: $i,SY1219: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1219 @ tc_HOL_Obool ) ) @ SY1218 ) @ SV120 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1219 @ tc_HOL_Obool ) ) @ SY1218 ) @ SV120 ) )
| ( SY1218 = SV120 ) )
| ~ ( ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1219 @ tc_HOL_Obool ) ) @ SY1218 ) @ SV120 ) )
| ( SY1218 = SV120 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1219 @ tc_HOL_Obool ) ) @ SY1218 ) @ SV120 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5820]) ).
thf(6067,plain,
! [SV121: $i] :
( ( ! [SY1220: $i,SY1221: $i,SY1222: $i] :
( ~ ( class_Orderings_Oord @ SY1222 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1221 @ SY1222 ) ) @ SY1220 ) @ SV121 ) )
| ! [SY1223: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1222 ) @ ( hAPP @ SY1220 @ SY1223 ) ) @ ( hAPP @ SV121 @ SY1223 ) ) ) )
| ~ ( ~ ! [SY1224: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1222 ) @ ( hAPP @ SY1220 @ SY1224 ) ) @ ( hAPP @ SV121 @ SY1224 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1221 @ SY1222 ) ) @ SY1220 ) @ SV121 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5821]) ).
thf(6068,plain,
! [SV122: $i] :
( ( ! [SY1225: $i,SY1226: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1226 @ SY1225 ) )
| ( hBOOL @ ( hAPP @ SY1226 @ ( c_Hilbert__Choice_OEps @ SV122 @ SY1226 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5822]) ).
thf(6069,plain,
! [SV123: $i] :
( ( ! [SY1227: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY1227 @ ( c_Hilbert__Choice_OEps @ SV123 @ SY1227 ) ) )
| ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SY1227 @ SX2 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SY1227 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SY1227 @ ( c_Hilbert__Choice_OEps @ SV123 @ SY1227 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5823]) ).
thf(6070,plain,
! [SV124: $i] :
( ( ! [SY1230: $i] :
( ~ ! [SY1231: $i] :
( ( hAPP @ SY1230 @ SY1231 )
= ( hAPP @ SV124 @ SY1231 ) )
| ( SY1230 = SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5824]) ).
thf(6071,plain,
! [SV125: $i] :
( ( ! [SY1232: $i,SY1233: $i,SY1234: $i,SY1235: $i] :
( ~ ( c_Fun_Oinj__on @ SY1235 @ SY1234 @ SY1233 @ SY1232 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1235 @ tc_HOL_Obool ) ) @ SV125 ) @ SY1232 ) )
| ( c_Fun_Oinj__on @ SY1235 @ SY1234 @ SY1233 @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5825]) ).
thf(6072,plain,
! [SV126: $i] :
( ( ! [SY1236: $i,SY1237: $i,SY1238: $i] :
( ~ ( class_Orderings_Oord @ SY1238 )
| ( SY1237 != SY1236 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1238 ) @ SY1236 ) @ SV126 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1238 ) @ SY1237 ) @ SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5826]) ).
thf(6073,plain,
! [SV127: $i] :
( ( ! [SY1239: $i,SY1240: $i,SY1241: $i,SY1242: $i,SY1243: $i,SY1244: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1244 @ SY1243 @ SY1242 @ SY1241 ) @ SY1240 )
!= SY1239 )
| ( ( hAPP @ SY1241 @ ( hAPP @ SY1240 @ SV127 ) )
= ( hAPP @ SY1239 @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5827]) ).
thf(6074,plain,
! [SV128: $i] :
( ( ! [SY1245: $i,SY1246: $i,SY1247: $i,SY1248: $i,SY1249: $i] :
~ ( ~ ( ( SY1249 != SY1248 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1247 @ SY1246 @ SY1245 @ SY1248 @ SV128 ) @ SY1249 )
= SV128 ) )
| ~ ( ~ ( ( SY1249 != SY1248 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1247 @ SY1246 @ SY1245 @ SY1248 @ SV128 ) @ SY1249 )
= ( hAPP @ SY1245 @ SY1249 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5828]) ).
thf(6075,plain,
! [SV129: $i] :
( ( ! [SY1250: $i,SY1251: $i,SY1252: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1252 ) @ SY1251 ) @ SY1250 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1252 ) @ SY1251 ) @ SV129 ) )
| ( SY1250 = SV129 ) )
| ~ ( ( SY1250 != SV129 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1252 ) @ SY1251 ) @ SY1250 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1252 ) @ SY1251 ) @ SV129 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5829]) ).
thf(6076,plain,
! [SV130: $i] :
( ( ! [SY1253: $i,SY1254: $i,SY1255: $i] :
( ~ ( class_Orderings_Opreorder @ SY1255 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1255 ) @ SY1254 ) @ SY1253 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1255 ) @ SY1253 ) @ SV130 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1255 ) @ SY1254 ) @ SV130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5830]) ).
thf(6077,plain,
! [SV131: $i] :
( ( ! [SY1256: $i,SY1257: $i,SY1258: $i] :
( ( SY1258 != SY1257 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1256 ) @ SY1258 ) @ SV131 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1256 ) @ SY1257 ) @ SV131 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1256 ) @ SY1257 ) @ SV131 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1256 ) @ SY1258 ) @ SV131 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5831]) ).
thf(6078,plain,
! [SV132: $i] :
( ( ! [SY1259: $i,SY1260: $i,SY1261: $i,SY1262: $i,SY1263: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1263 ) @ SY1262 ) @ SY1261 )
!= SY1260 )
| ( SY1259
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1263 ) @ SY1261 ) @ SV132 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1263 ) @ SY1262 ) @ SY1259 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1263 ) @ SY1260 ) @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5832]) ).
thf(6079,plain,
! [SV133: $i] :
( ( ! [SY1264: $i,SY1265: $i,SY1266: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1266 ) @ SY1265 ) @ SY1264 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1266 ) @ SV133 ) @ SY1264 ) )
| ( SY1265 = SV133 ) )
| ~ ( ( SY1265 != SV133 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1266 ) @ SY1265 ) @ SY1264 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1266 ) @ SV133 ) @ SY1264 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5833]) ).
thf(6080,plain,
! [SV134: $i] :
( ( ! [SY1267: $i,SY1268: $i,SY1269: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1269 @ tc_HOL_Obool ) ) @ SY1268 ) @ SY1267 ) )
| ~ ( hBOOL @ ( hAPP @ SY1268 @ SV134 ) )
| ( hBOOL @ ( hAPP @ SY1267 @ SV134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5834]) ).
thf(6081,plain,
! [SV135: $i] :
( ( ! [SY1270: $i,SY1271: $i,SY1272: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SY1272 @ SY1271 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1271 @ SY1270 ) @ SV135 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1271 @ SV135 ) @ SY1270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5835]) ).
thf(6082,plain,
! [SV136: $i] :
( ( ! [SY1273: $i,SY1274: $i,SY1275: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY1275 @ SY1274 ) @ SY1273 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY1275 @ SY1274 ) @ SV136 ) )
| ( SY1273 = SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5836]) ).
thf(6083,plain,
! [SV137: $i] :
( ( ! [SY1276: $i,SY1277: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1277 ) @ SY1276 ) @ SV137 ) )
| ( hBOOL @ ( hAPP @ SV137 @ SY1276 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV137 @ SY1276 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1277 ) @ SY1276 ) @ SV137 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5837]) ).
thf(6084,plain,
! [SV138: $i] :
( ( ! [SY1278: $i,SY1279: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1279 @ ( tc_fun @ SY1279 @ tc_HOL_Obool ) ) ) @ SY1278 ) @ SV138 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1279 @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ SY1279 @ SV138 ) ) @ ( c_Wellfounded_Oaccp @ SY1279 @ SY1278 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5838]) ).
thf(6085,plain,
! [SV139: $i] :
( ( ! [SY1280: $i,SY1281: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1281 @ tc_HOL_Obool ) ) @ SY1280 ) @ SV139 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1281 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1281 @ tc_HOL_Obool ) ) @ SV139 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1281 @ tc_HOL_Obool ) ) @ SY1280 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5839]) ).
thf(6086,plain,
! [SV140: $i] :
( ( ! [SY1282: $i,SY1283: $i,SY1284: $i,SY1285: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1285 @ SY1284 ) @ SY1283 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1282 @ SV140 @ SY1285 ) @ SY1283 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5840]) ).
thf(6087,plain,
! [SV141: $i] :
( ( ! [SY1286: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SY1286 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV141 ) )
| ( SY1286 = SV141 ) )
| ~ ( ( SY1286 != SV141 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SY1286 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV141 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5841]) ).
thf(6088,plain,
! [SV142: $i] :
( ( ! [SY1287: $i,SY1288: $i,SY1289: $i,SY1290: $i,SY1291: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1291 @ ( tc_fun @ SY1290 @ tc_HOL_Obool ) ) ) @ SY1289 ) @ SY1288 ) @ SY1287 ) @ SV142 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1289 @ SY1287 ) @ SV142 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1288 @ SY1287 ) @ SV142 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5842]) ).
thf(6089,plain,
! [SV143: $i] :
( ( ! [SY1292: $i,SY1293: $i,SY1294: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1294 @ tc_HOL_Obool ) ) @ SY1293 ) @ SY1292 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1294 @ tc_HOL_Obool ) ) @ SY1293 ) @ SV143 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1294 @ tc_HOL_Obool ) ) @ SY1293 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1294 @ tc_HOL_Obool ) ) @ SY1292 ) @ SV143 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5843]) ).
thf(6090,plain,
! [SV144: $i] :
( ( ! [SY1295: $i,SY1296: $i] :
~ ( ~ ( ( SY1296 != SY1295 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SY1296 ) @ SY1295 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SY1295 ) @ SY1296 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SY1296 ) @ SY1295 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SY1295 ) @ SY1296 ) ) )
| ( SY1296 = SY1295 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5844]) ).
thf(6091,plain,
! [SV145: $i] :
( ( ! [SY1297: $i,SY1298: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SY1298 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SY1297 ) @ SV145 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1298 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SY1298 @ tc_HOL_Obool ) @ SV145 ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SY1298 @ tc_HOL_Obool ) @ SY1297 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5845]) ).
thf(6092,plain,
! [SV146: $i] :
( ( ! [SY1299: $i,SY1300: $i,SY1301: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1301 @ SY1300 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1299 @ tc_HOL_Obool ) ) @ SY1301 ) @ SV146 ) )
| ( hBOOL @ ( hAPP @ SV146 @ SY1300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5846]) ).
thf(6093,plain,
! [SV147: $i] :
( ( ! [SY1302: $i,SY1303: $i,SY1304: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1304 @ tc_HOL_Obool ) ) @ SY1303 ) @ SY1302 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1304 @ tc_HOL_Obool ) ) @ SY1302 ) @ SV147 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1304 @ tc_HOL_Obool ) ) @ SY1303 ) @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5847]) ).
thf(6094,plain,
! [SV148: $i] :
( ( ! [SY1305: $i,SY1306: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SY1306 ) @ SY1305 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SY1305 ) @ SV148 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SY1306 ) @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5848]) ).
thf(6095,plain,
! [SV149: $i] :
( ( ! [SY1307: $i,SY1308: $i,SY1309: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1309 @ SY1308 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1307 @ tc_HOL_Obool ) ) @ SY1309 ) @ SV149 ) @ SY1308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5849]) ).
thf(6096,plain,
! [SV150: $i] :
( ( ! [SY1310: $i,SY1311: $i,SY1312: $i,SY1313: $i] :
( ~ ( class_Orderings_Oord @ SY1313 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1312 @ SY1313 ) ) @ SY1311 ) @ SY1310 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1313 ) @ ( hAPP @ SY1311 @ SV150 ) ) @ ( hAPP @ SY1310 @ SV150 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5850]) ).
thf(6097,plain,
! [SV151: $i] :
( ( ! [SY1314: $i,SY1315: $i,SY1316: $i,SY1317: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1317 @ SY1316 ) @ SY1315 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1314 @ SV151 @ SY1317 ) @ SY1316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5851]) ).
thf(6098,plain,
! [SV152: $i] :
( ( ! [SY1318: $i,SY1319: $i,SY1320: $i,SY1321: $i,SY1322: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1322 @ SY1321 ) @ SY1320 ) @ SY1319 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1322 @ SY1321 ) @ SY1318 ) @ SV152 ) )
| ~ ( ( SY1320 != SY1318 )
| ( SY1319 != SV152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5852]) ).
thf(6099,plain,
! [SV153: $i] :
( ( ! [SY1323: $i,SY1324: $i,SY1325: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1325 @ tc_HOL_Obool ) ) @ SY1324 ) @ SY1323 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1325 ) @ SV153 ) @ SY1324 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1325 ) @ SV153 ) @ SY1323 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5853]) ).
thf(6100,plain,
! [SV154: $i] :
( ( ! [SY1326: $i,SY1327: $i,SY1328: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1328 @ tc_HOL_Obool ) ) @ SY1327 ) @ SY1326 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1328 ) @ SV154 ) @ SY1327 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1328 ) @ SV154 ) @ SY1326 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5854]) ).
thf(6101,plain,
! [SV155: $i] :
( ( ! [SY1329: $i,SY1330: $i,SY1331: $i,SY1332: $i,SY1333: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1333 @ SY1332 ) @ SY1331 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1330 @ SY1332 ) @ SY1331 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1329 @ ( tc_fun @ SV155 @ tc_HOL_Obool ) ) ) @ SY1330 ) @ SY1333 ) @ SY1332 ) @ SY1331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5855]) ).
thf(6102,plain,
! [SV156: $i] :
( ( ! [SY1334: $i,SY1335: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1335 @ tc_HOL_Obool ) ) @ SY1334 ) @ SV156 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1335 @ tc_HOL_Obool ) ) @ SY1334 ) @ SV156 ) )
| ~ ( ( SY1334 != SV156 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1335 @ tc_HOL_Obool ) ) @ SY1334 ) @ SV156 ) )
| ~ ( ( SY1334 != SV156 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1335 @ tc_HOL_Obool ) ) @ SY1334 ) @ SV156 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5856]) ).
thf(6103,plain,
! [SV157: $i] :
( ( ! [SY1336: $i,SY1337: $i,SY1338: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1338 @ tc_HOL_Obool ) ) @ SY1337 ) @ SY1336 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1338 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1338 ) @ SV157 ) @ SY1337 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1338 ) @ SV157 ) @ SY1336 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5857]) ).
thf(6104,plain,
! [SV158: $i] :
( ( ! [SY1339: $i] :
( ~ ( class_Orderings_Oord @ SY1339 )
| ( class_Orderings_Oord @ ( tc_fun @ SV158 @ SY1339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5858]) ).
thf(6105,plain,
! [SV159: $i] :
( ( ! [SY1340: $i,SY1341: $i,SY1342: $i,SY1343: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1343 @ SY1342 @ SY1341 ) @ SY1340 ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1341 @ SV159 ) @ SY1340 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1341 @ SV159 ) @ SY1340 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1343 @ SY1342 @ SY1341 ) @ SY1340 ) @ SV159 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5859]) ).
thf(6106,plain,
! [SV160: $i] :
( ( ! [SY1344: $i,SY1345: $i,SY1346: $i,SY1347: $i] :
( ~ ( c_Predicate_Otransp @ SY1347 @ SY1346 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1346 @ SY1345 ) @ SY1344 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1346 @ SY1344 ) @ SV160 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1346 @ SY1345 ) @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5860]) ).
thf(6107,plain,
! [SV161: $i] :
( ( ! [SY1348: $i,SY1349: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1349 @ tc_HOL_Obool ) ) @ SY1348 )
!= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1349 @ tc_HOL_Obool ) ) @ SV161 ) )
| ( SY1348 = SV161 ) )
| ~ ( ( SY1348 != SV161 )
| ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1349 @ tc_HOL_Obool ) ) @ SY1348 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1349 @ tc_HOL_Obool ) ) @ SV161 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5861]) ).
thf(6108,plain,
! [SV162: $i] :
( ( ! [SY1350: $i,SY1351: $i,SY1352: $i,SY1353: $i] :
( ~ ( class_Orderings_Oord @ SY1353 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1352 @ SY1353 ) ) @ SY1351 ) @ SY1350 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1353 ) @ ( hAPP @ SY1351 @ SV162 ) ) @ ( hAPP @ SY1350 @ SV162 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5862]) ).
thf(6109,plain,
! [SV163: $i] :
( ( ! [SY1354: $i,SY1355: $i,SY1356: $i] :
( ~ ( class_Orderings_Oorder @ SY1356 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1356 ) @ SY1355 ) @ SY1354 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1356 ) @ SV163 ) @ SY1355 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1356 ) @ SV163 ) @ SY1354 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5863]) ).
thf(6110,plain,
! [SV164: $i] :
( ( ! [SY1357: $i] :
~ ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SY1357 )
!= ( hAPP @ c_Nat_OSuc @ SV164 ) )
| ( SY1357 = SV164 ) )
| ~ ( ( SY1357 != SV164 )
| ( ( hAPP @ c_Nat_OSuc @ SY1357 )
= ( hAPP @ c_Nat_OSuc @ SV164 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5864]) ).
thf(6111,plain,
! [SV165: $i] :
( ( ! [SY1358: $i,SY1359: $i,SY1360: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1360 @ SY1359 ) @ SY1358 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1359 @ SV165 ) @ SY1358 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1360 @ SY1359 ) @ SV165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5865]) ).
thf(6112,plain,
! [SV166: $i] :
( ( ! [SY1361: $i,SY1362: $i,SY1363: $i] :
( ~ ( class_Orderings_Oord @ SY1363 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1363 ) @ SY1362 ) @ SY1361 ) )
| ( SY1361 != SV166 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1363 ) @ SY1362 ) @ SV166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5866]) ).
thf(6113,plain,
! [SV167: $i] :
( ( ! [SY1364: $i,SY1365: $i,SY1366: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1366 @ tc_HOL_Obool ) ) @ SY1365 ) @ SY1364 ) @ SV167 ) )
| ( hBOOL @ ( hAPP @ SY1364 @ SV167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5867]) ).
thf(6114,plain,
! [SV168: $i] :
( ( ! [SY1367: $i,SY1368: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1368 @ tc_HOL_Obool ) ) @ SY1367 ) @ SV168 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1368 @ tc_HOL_Obool ) ) @ SY1367 ) @ SV168 )
= SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5868]) ).
thf(6115,plain,
! [SV169: $i] :
( ( ! [SY1369: $i,SY1370: $i,SY1371: $i,SY1372: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1372 @ tc_HOL_Obool ) ) @ SY1371 ) @ ( hAPP @ ( c_Set_Oimage @ SY1370 @ SY1372 @ SY1369 ) @ SV169 ) ) )
| ~ ! [SY1373: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1370 @ tc_HOL_Obool ) ) @ SY1373 ) @ SV169 ) )
| ( SY1371
!= ( hAPP @ ( c_Set_Oimage @ SY1370 @ SY1372 @ SY1369 ) @ SY1373 ) ) ) )
| ~ ( ~ ~ ! [SY1374: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1370 @ tc_HOL_Obool ) ) @ SY1374 ) @ SV169 ) )
| ( SY1371
!= ( hAPP @ ( c_Set_Oimage @ SY1370 @ SY1372 @ SY1369 ) @ SY1374 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1372 @ tc_HOL_Obool ) ) @ SY1371 ) @ ( hAPP @ ( c_Set_Oimage @ SY1370 @ SY1372 @ SY1369 ) @ SV169 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5869]) ).
thf(6116,plain,
! [SV170: $i] :
( ( ! [SY1375: $i,SY1376: $i,SY1377: $i,SY1378: $i,SY1379: $i] :
( ( SY1379 != SY1378 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1377 @ SY1376 @ SY1375 ) @ SV170 ) @ SY1379 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1377 @ SY1376 @ SY1375 ) @ SV170 ) @ SY1378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5870]) ).
thf(6117,plain,
! [SV171: $i] :
( ( ! [SY1380: $i,SY1381: $i,SY1382: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1382 @ SY1381 ) )
| ( hBOOL @ ( hAPP @ SY1380 @ SY1381 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV171 @ tc_HOL_Obool ) ) @ SY1380 ) @ SY1382 ) @ SY1381 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5871]) ).
thf(6118,plain,
! [SV172: $i] :
( ( ! [SY1383: $i,SY1384: $i,SY1385: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1385 @ tc_HOL_Obool ) ) @ SY1384 ) @ SY1383 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1385 @ tc_HOL_Obool ) ) @ SY1383 ) @ SV172 ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1385 @ tc_HOL_Obool ) ) @ SY1383 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1385 @ tc_HOL_Obool ) ) @ SV172 ) @ SY1384 ) )
= SY1384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5872]) ).
thf(6119,plain,
! [SV173: $i] :
( ( ! [SY1386: $i,SY1387: $i] :
( ~ ( class_Orderings_Olinorder @ SY1387 )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1387 ) @ SY1386 ) @ SV173 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1387 ) @ SV173 ) @ SY1386 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5873]) ).
thf(6120,plain,
! [SV174: $i] :
( ( ! [SY1388: $i,SY1389: $i,SY1390: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1390 @ SY1389 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1388 @ tc_HOL_Obool ) ) @ SV174 ) @ SY1390 ) @ SY1389 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5874]) ).
thf(6121,plain,
! [SV175: $i] :
( ( ! [SY1391: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SY1391 )
| ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV175 @ SY1391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5875]) ).
thf(6122,plain,
! [SV176: $i] :
( ( ! [SY1392: $i] :
( ~ ( class_Groups_Ominus @ SY1392 )
| ( class_Groups_Ominus @ ( tc_fun @ SV176 @ SY1392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5876]) ).
thf(6123,plain,
! [SV177: $i] :
( ( ! [SY1393: $i,SY1394: $i,SY1395: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1395 @ tc_HOL_Obool ) ) @ SY1394 ) @ SY1393 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1395 ) @ SV177 ) @ SY1394 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1395 ) @ SV177 ) @ SY1393 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5877]) ).
thf(6124,plain,
! [SV178: $i] :
( ( ! [SY1396: $i,SY1397: $i,SY1398: $i,SY1399: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1399 @ tc_HOL_Obool ) ) @ SY1398 ) @ SY1397 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1399 @ tc_HOL_Obool ) ) @ SY1396 ) @ SV178 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1399 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1399 @ tc_HOL_Obool ) ) @ SY1398 ) @ SY1396 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1399 @ tc_HOL_Obool ) ) @ SY1397 ) @ SV178 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5878]) ).
thf(6125,plain,
! [SV179: $i] :
( ( ! [SY1400: $i,SY1401: $i,SY1402: $i,SY1403: $i,SY1404: $i] :
( ~ ( ( SY1404 != SY1403 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1402 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1402 @ SY1401 ) @ SY1404 ) @ SY1400 ) ) @ SY1403 ) @ SV179 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1402 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1402 @ SY1401 ) @ SY1403 ) @ SV179 ) ) @ SY1404 ) @ SY1400 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5879]) ).
thf(6126,plain,
! [SV180: $i] :
( ( ! [SY1405: $i,SY1406: $i,SY1407: $i,SY1408: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1408 @ tc_HOL_Obool ) ) @ SY1407 ) @ SY1406 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1405 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ SY1408 @ SY1405 @ SV180 ) @ SY1407 ) ) @ ( hAPP @ ( c_Set_Oimage @ SY1408 @ SY1405 @ SV180 ) @ SY1406 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5880]) ).
thf(6127,plain,
! [SV181: $i] :
( ( ! [SY1409: $i,SY1410: $i,SY1411: $i,SY1412: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1412 @ SY1411 @ SY1410 ) @ SY1409 ) @ SV181 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1410 @ SV181 ) @ SY1409 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1410 @ SV181 ) @ SY1409 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1412 @ SY1411 @ SY1410 ) @ SY1409 ) @ SV181 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5881]) ).
thf(6128,plain,
! [SV182: $i] :
( ( ! [SY1413: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SY1413 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV182 ) )
| ( SY1413 = SV182 ) )
| ~ ( ( SY1413 != SV182 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SY1413 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV182 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5882]) ).
thf(6129,plain,
! [SV183: $i] :
( ( ! [SY1414: $i,SY1415: $i,SY1416: $i,SY1417: $i,SY1418: $i,SY1419: $i,SY1420: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1420 @ SY1419 @ SY1418 @ SY1417 ) @ SY1416 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY1415 @ SY1419 @ SY1418 @ SY1414 ) @ SV183 ) )
| ! [SY1421: $i] :
( ( hAPP @ SY1417 @ ( hAPP @ SY1416 @ SY1421 ) )
= ( hAPP @ SY1414 @ ( hAPP @ SV183 @ SY1421 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5883]) ).
thf(6130,plain,
! [SV184: $i] :
( ( ! [SY1422: $i] :
~ ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SY1422 @ SV184 )
| ! [SY1423: $i,SY1424: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1423 ) @ SY1424 ) )
| ( ( hAPP @ SV184 @ SY1423 )
= ( hAPP @ SV184 @ SY1424 ) ) )
| ~ ( ( ( hAPP @ SV184 @ SY1423 )
!= ( hAPP @ SV184 @ SY1424 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1423 ) @ SY1424 ) ) ) ) )
| ~ ( ~ ! [SY1425: $i,SY1426: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1425 ) @ SY1426 ) )
| ( ( hAPP @ SV184 @ SY1425 )
= ( hAPP @ SV184 @ SY1426 ) ) )
| ~ ( ( ( hAPP @ SV184 @ SY1425 )
!= ( hAPP @ SV184 @ SY1426 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1425 ) @ SY1426 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SY1422 @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5884]) ).
thf(6131,plain,
! [SV185: $i] :
( ( ! [SY1427: $i,SY1428: $i,SY1429: $i,SY1430: $i] :
( ( ( hAPP @ SY1430 @ SY1429 )
!= SY1428 )
| ( ( c_Fun_Ofun__upd @ SY1427 @ SV185 @ SY1430 @ SY1429 @ SY1428 )
= SY1430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5885]) ).
thf(6132,plain,
! [SV186: $i] :
( ( ! [SY1431: $i,SY1432: $i,SY1433: $i,SY1434: $i,SY1435: $i,SY1436: $i,SY1437: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1437 @ SY1436 ) @ SY1435 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1434 @ SY1435 ) @ SY1433 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY1432 @ SY1431 @ SV186 @ SY1437 @ SY1434 ) @ SY1436 ) @ SY1433 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5886]) ).
thf(6133,plain,
! [SV187: $i] :
( ( ! [SY1438: $i,SY1439: $i,SY1440: $i,SY1441: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1441 ) @ SY1440 ) @ SY1439 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1441 ) @ SY1438 ) @ SV187 ) )
| ~ ( ( SY1440 != SY1438 )
| ( SY1439 != SV187 ) ) )
| ~ ( ~ ~ ( ( SY1440 != SY1438 )
| ( SY1439 != SV187 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1441 ) @ SY1440 ) @ SY1439 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1441 ) @ SY1438 ) @ SV187 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5887]) ).
thf(6134,plain,
! [SV188: $i] :
( ( ! [SY1442: $i] :
( ( SY1442 != SV188 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SY1442 ) @ SV188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5888]) ).
thf(6135,plain,
! [SV189: $i] :
( ( ! [SY1443: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SY1443 ) @ SV189 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV189 ) @ SY1443 ) )
| ( SY1443 = SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5889]) ).
thf(6136,plain,
! [SV190: $i] :
( ( ! [SY1444: $i,SY1445: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1445 @ tc_HOL_Obool ) ) @ SY1444 ) @ SV190 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1445 @ tc_HOL_Obool ) ) @ SV190 ) @ SY1444 )
= SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5890]) ).
thf(6137,plain,
! [SV191: $i] :
( ( ! [SY1446: $i,SY1447: $i,SY1448: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1448 @ tc_HOL_Obool ) ) @ SY1447 ) @ SY1446 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1448 @ tc_HOL_Obool ) ) @ SY1446 ) @ SV191 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1448 @ tc_HOL_Obool ) ) @ SY1447 ) @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5891]) ).
thf(6138,plain,
! [SV192: $i] :
( ( ! [SY1449: $i,SY1450: $i,SY1451: $i,SY1452: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1452 @ tc_HOL_Obool ) ) @ SY1451 ) @ SY1450 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1452 @ tc_HOL_Obool ) ) @ SY1449 ) @ SV192 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1452 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1452 @ tc_HOL_Obool ) ) @ SY1451 ) @ SV192 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1452 @ tc_HOL_Obool ) ) @ SY1450 ) @ SY1449 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5892]) ).
thf(6139,plain,
! [SV193: $i] :
( ( ! [SY1453: $i,SY1454: $i] :
( ( SY1454 != SY1453 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV193 @ tc_HOL_Obool ) ) @ SY1454 ) @ SY1453 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5893]) ).
thf(6140,plain,
! [SV194: $i] :
( ( ! [SY1455: $i,SY1456: $i] :
( SY1456
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1455 ) @ SV194 ) @ SY1456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5894]) ).
thf(6141,plain,
! [SV195: $i] :
( ( ! [SY1457: $i] :
( ~ ( class_Orderings_Obot @ SY1457 )
| ( class_Orderings_Obot @ ( tc_fun @ SV195 @ SY1457 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5895]) ).
thf(6142,plain,
! [SV196: $i] :
( ( ! [SY1458: $i,SY1459: $i,SY1460: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1460 @ tc_HOL_Obool ) ) @ SY1459 ) @ SY1458 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1460 @ tc_HOL_Obool ) ) @ SY1458 ) @ SV196 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1460 @ tc_HOL_Obool ) ) @ SY1459 ) @ SV196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5896]) ).
thf(6143,plain,
! [SV197: $i] :
( ( ! [SY1461: $i,SY1462: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SY1462 @ SY1461 ) @ SV197 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1461 @ SV197 ) @ SV197 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1461 @ SV197 ) @ SV197 ) )
| ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SY1462 @ SY1461 ) @ SV197 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5897]) ).
thf(6144,plain,
! [SV198: $i] :
( ( ! [SY1463: $i,SY1464: $i] :
( ~ ( class_Orderings_Oorder @ SY1464 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1464 ) @ SY1463 ) @ SV198 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1464 ) @ SV198 ) @ SY1463 ) )
| ( SY1463 = SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5898]) ).
thf(6145,plain,
! [SV199: $i] :
( ( ! [SY1465: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1465 @ tc_HOL_Obool ) ) @ SV199 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1465 @ tc_HOL_Obool ) ) ) )
| ( SV199
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1465 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV199
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1465 @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1465 @ tc_HOL_Obool ) ) @ SV199 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1465 @ tc_HOL_Obool ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5899]) ).
thf(6146,plain,
! [SV200: $i] :
( ( ! [SY1466: $i,SY1467: $i,SY1468: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1468 @ tc_HOL_Obool ) ) @ SY1467 ) @ SY1466 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1468 @ tc_HOL_Obool ) ) @ SV200 ) @ SY1466 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1468 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1468 @ tc_HOL_Obool ) ) @ SY1467 ) @ SV200 ) ) @ SY1466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5900]) ).
thf(6147,plain,
! [SV201: $i] :
( ( ! [SY1469: $i,SY1470: $i,SY1471: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1471 @ SY1470 @ SY1469 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1471 @ SV201 @ SY1470 )
| ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1471 @ SV201 @ SY1469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5901]) ).
thf(6148,plain,
! [SV202: $i] :
( ( ! [SY1472: $i,SY1473: $i] :
~ ( ~ ( ~ ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY1473 @ SX3 ) )
| ! [SY1475: $i,SY1476: $i] : ( hBOOL @ ( hAPP @ SY1473 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1472 @ SV202 ) @ SY1475 ) @ SY1476 ) ) ) )
| ~ ( ~ ! [SY1477: $i,SY1478: $i] : ( hBOOL @ ( hAPP @ SY1473 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1472 @ SV202 ) @ SY1477 ) @ SY1478 ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY1473 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5902]) ).
thf(6149,plain,
! [SV203: $i] :
( ( ! [SY1480: $i,SY1481: $i] :
( ~ ( class_Orderings_Oorder @ SY1481 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1481 ) @ SY1480 ) @ SV203 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1481 ) @ SV203 ) @ SY1480 ) )
| ( SV203 = SY1480 ) )
| ~ ( ( SV203 != SY1480 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1481 ) @ SV203 ) @ SY1480 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5903]) ).
thf(6150,plain,
! [SV204: $i] :
( ( ! [SY1482: $i,SY1483: $i,SY1484: $i,SY1485: $i,SY1486: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1486 @ ( tc_fun @ SY1485 @ tc_HOL_Obool ) ) ) @ SY1484 ) @ SY1483 ) @ SY1482 ) @ SV204 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1484 @ SY1482 ) @ SV204 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1483 @ SY1482 ) @ SV204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5904]) ).
thf(6151,plain,
! [SV205: $i] :
( ( ! [SY1487: $i,SY1488: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SY1488 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SY1487 ) @ SV205 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1488 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SY1488 @ tc_HOL_Obool ) @ SY1487 ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SY1488 @ tc_HOL_Obool ) @ SV205 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5905]) ).
thf(6152,plain,
! [SV206: $i] :
( ( ! [SY1489: $i] :
( ~ ( class_Orderings_Opreorder @ SY1489 )
| ( class_Orderings_Opreorder @ ( tc_fun @ SV206 @ SY1489 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5906]) ).
thf(6153,plain,
! [SV207: $i] :
( ( ! [SY1490: $i,SY1491: $i] :
( ~ ( class_Orderings_Opreorder @ SY1491 )
| ( SY1490 != SV207 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1491 ) @ SY1490 ) @ SV207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5907]) ).
thf(6154,plain,
! [SV208: $i] :
( ( ! [SY1492: $i,SY1493: $i,SY1494: $i,SY1495: $i,SY1496: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1496 @ SY1495 ) @ SY1494 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1493 @ ( tc_fun @ SY1492 @ tc_HOL_Obool ) ) ) @ SY1496 ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV208 @ SY1495 ) @ SY1494 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5908]) ).
thf(6155,plain,
! [SV209: $i] :
( ( ! [SY1497: $i,SY1498: $i,SY1499: $i,SY1500: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1500 @ SY1499 @ SY1498 )
| ( ( hAPP @ ( hAPP @ SY1498 @ SY1497 ) @ ( hAPP @ ( hAPP @ SY1498 @ SY1497 ) @ SV209 ) )
= ( hAPP @ ( hAPP @ SY1498 @ SY1497 ) @ SV209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5909]) ).
thf(6156,plain,
! [SV210: $i] :
( ( ! [SY1501: $i,SY1502: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1502 ) @ SY1501 ) @ SV210 )
!= SV210 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5910]) ).
thf(6157,plain,
! [SV211: $i] :
( ( ! [SY1503: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SY1503 )
| ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV211 @ SY1503 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5911]) ).
thf(6158,plain,
! [SV212: $i] :
( ( ! [SY1504: $i,SY1505: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY1505 ) @ SY1504 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1505 @ tc_HOL_Obool ) ) @ SV212 ) @ SY1504 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY1505 ) @ SV212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5912]) ).
thf(6159,plain,
! [SV213: $i] :
( ( ! [SY1506: $i,SY1507: $i,SY1508: $i] :
( ~ ( class_Orderings_Oorder @ SY1508 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1508 ) @ SY1507 ) @ SY1506 ) )
| ( SY1507 != SV213 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1508 ) @ SV213 ) @ SY1506 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5913]) ).
thf(6160,plain,
! [SV214: $i] :
( ( ! [SY1509: $i,SY1510: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SY1510 ) @ SY1509 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SY1509 ) @ SV214 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SY1510 ) @ SV214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5914]) ).
thf(6161,plain,
! [SV215: $i] :
( ( ! [SY1511: $i,SY1512: $i,SY1513: $i] :
( ( SY1513 != SY1512 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1511 ) @ SY1512 ) @ SV215 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1511 ) @ SY1513 ) @ SV215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5915]) ).
thf(6162,plain,
! [SV216: $i] :
( ( ! [SY1514: $i,SY1515: $i,SY1516: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1516 ) @ SY1515 ) @ SY1514 ) @ SV216 ) )
| ( SY1515 = SV216 )
| ( hBOOL @ ( hAPP @ SY1514 @ SV216 ) ) )
| ~ ( ~ ( ( SY1515 = SV216 )
| ( hBOOL @ ( hAPP @ SY1514 @ SV216 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1516 ) @ SY1515 ) @ SY1514 ) @ SV216 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5916]) ).
thf(6163,plain,
! [SV217: $i] :
( ( ! [SY1517: $i,SY1518: $i,SY1519: $i,SY1520: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1520 ) @ SY1519 ) @ SY1518 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1520 ) @ SY1517 ) @ SV217 ) )
| ~ ! [SY1521: $i] :
~ ( ~ ( ( SY1519
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1520 ) @ SY1517 ) @ SY1521 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1520 ) @ SY1521 ) @ SY1518 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1520 ) @ SY1519 ) @ SY1521 )
!= SY1517 )
| ( SY1518
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1520 ) @ SY1521 ) @ SV217 ) ) ) ) )
| ~ ( ~ ~ ! [SY1522: $i] :
~ ( ~ ( ( SY1519
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1520 ) @ SY1517 ) @ SY1522 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1520 ) @ SY1522 ) @ SY1518 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1520 ) @ SY1519 ) @ SY1522 )
!= SY1517 )
| ( SY1518
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1520 ) @ SY1522 ) @ SV217 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1520 ) @ SY1519 ) @ SY1518 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1520 ) @ SY1517 ) @ SV217 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5917]) ).
thf(6164,plain,
! [SV218: $i] :
( ( ! [SY1523: $i] :
( ~ ~ ( ~ ( class_Finite__Set_Ofinite @ SY1523 )
| ~ ( class_Finite__Set_Ofinite @ SV218 ) )
| ( class_Finite__Set_Ofinite @ ( tc_fun @ SY1523 @ SV218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5918]) ).
thf(6165,plain,
! [SV219: $i] :
( ( ! [SY1524: $i,SY1525: $i,SY1526: $i,SY1527: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1527 @ SY1526 @ SY1525 ) @ SY1524 ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1525 @ SV219 ) @ SY1524 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5919]) ).
thf(6166,plain,
! [SV220: $i] :
( ( ! [SY1528: $i,SY1529: $i] :
( ( SY1529 != SY1528 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV220 @ tc_HOL_Obool ) ) @ SY1528 ) @ SY1529 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5920]) ).
thf(6167,plain,
! [SV221: $i] :
( ( ! [SY1530: $i,SY1531: $i,SY1532: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY1532 @ SY1531 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1531 @ SY1530 ) @ SV221 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1531 @ SV221 ) @ SY1530 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5921]) ).
thf(6168,plain,
! [SV222: $i] :
( ( ! [SY1533: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ SY1533 )
| ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SV222 @ SY1533 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5922]) ).
thf(6169,plain,
! [SV223: $i] :
( ( ! [SY1534: $i,SY1535: $i,SY1536: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1536 @ SY1535 @ SY1534 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1536 ) @ tc_HOL_Obool ) ) @ SV223 ) @ SY1534 ) )
| ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1536 @ SY1535 @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5923]) ).
thf(6170,plain,
! [SV224: $i] :
( ( ! [SY1537: $i,SY1538: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY1538 ) @ SY1537 )
!= SV224 )
| ( SY1537
= ( hAPP @ ( c_List_Orev @ SY1538 ) @ SV224 ) ) )
| ~ ( ( SY1537
!= ( hAPP @ ( c_List_Orev @ SY1538 ) @ SV224 ) )
| ( ( hAPP @ ( c_List_Orev @ SY1538 ) @ SY1537 )
= SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5924]) ).
thf(6171,plain,
! [SV225: $i] :
( ( ! [SY1539: $i,SY1540: $i,SY1541: $i,SY1542: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY1542 @ SY1541 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1541 @ SY1540 ) @ SY1539 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1541 @ SY1539 ) @ SV225 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1541 @ SY1540 ) @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5925]) ).
thf(6172,plain,
! [SV226: $i] :
( ( ! [SY1543: $i,SY1544: $i,SY1545: $i,SY1546: $i,SY1547: $i,SY1548: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY1548 @ SY1547 @ SY1546 @ SY1545 @ SY1544 ) @ SY1543 ) @ SV226 ) )
| ~ ! [SY1549: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1545 @ SY1543 ) @ SY1549 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1544 @ SY1549 ) @ SV226 ) ) ) )
| ~ ( ~ ~ ! [SY1550: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1545 @ SY1543 ) @ SY1550 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1544 @ SY1550 ) @ SV226 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY1548 @ SY1547 @ SY1546 @ SY1545 @ SY1544 ) @ SY1543 ) @ SV226 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5926]) ).
thf(6173,plain,
! [SV227: $i] :
( ( ! [SY1551: $i,SY1552: $i,SY1553: $i,SY1554: $i,SY1555: $i,SY1556: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY1556 @ SY1555 @ SY1554 @ SY1553 @ SY1552 @ SY1551 )
| ( ( hAPP @ ( hAPP @ SY1554 @ SV227 ) @ SV227 )
= SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5927]) ).
thf(6174,plain,
! [SV228: $i] :
( ( ! [SY1557: $i,SY1558: $i,SY1559: $i,SY1560: $i,SY1561: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1561 @ SY1560 ) @ SY1559 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1558 @ ( tc_fun @ SY1557 @ tc_HOL_Obool ) ) ) @ SY1561 ) @ SV228 ) @ SY1560 ) @ SY1559 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5928]) ).
thf(6175,plain,
! [SV229: $i] :
( ( ! [SY1562: $i,SY1563: $i,SY1564: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1564 ) @ SY1563 ) @ SY1562 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1564 @ tc_HOL_Obool ) ) @ SY1562 ) @ SV229 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1564 ) @ SY1563 ) @ SV229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5929]) ).
thf(6176,plain,
! [SV230: $i] :
( ( ! [SY1565: $i,SY1566: $i,SY1567: $i] :
( ~ ( class_Orderings_Oorder @ SY1567 )
| ( SY1566 != SY1565 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1567 ) @ SV230 ) @ SY1565 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1567 ) @ SV230 ) @ SY1566 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5930]) ).
thf(6177,plain,
! [SV231: $i] :
( ( ! [SY1568: $i,SY1569: $i] :
( ~ ( class_Orderings_Oorder @ SY1569 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1569 ) @ SY1568 ) @ SV231 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1569 ) @ SV231 ) @ SY1568 ) )
| ( SV231 = SY1568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5931]) ).
thf(6178,plain,
! [SV232: $i] :
( ( ! [SY1570: $i] :
( ~ ( class_Orderings_Oorder @ SY1570 )
| ( class_Orderings_Oorder @ ( tc_fun @ SV232 @ SY1570 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5932]) ).
thf(6179,plain,
! [SV233: $i] :
( ( ! [SY1571: $i,SY1572: $i,SY1573: $i,SY1574: $i,SY1575: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1575 @ SY1574 ) @ SY1573 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1572 @ ( tc_fun @ SY1571 @ tc_HOL_Obool ) ) ) @ SV233 ) @ SY1575 ) @ SY1574 ) @ SY1573 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5933]) ).
thf(6180,plain,
! [SV234: $i] :
( ( ! [SY1576: $i,SY1577: $i,SY1578: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1578 @ tc_HOL_Obool ) ) @ SY1577 ) @ SY1576 ) @ SV234 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SY1577 @ SV234 ) )
| ( hBOOL @ ( hAPP @ SY1576 @ SV234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5934]) ).
thf(6181,plain,
! [SV235: $i] :
( ( ! [SY1579: $i,SY1580: $i,SY1581: $i,SY1582: $i,SY1583: $i,SY1584: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1584 @ SY1583 @ SY1582 @ SY1581 @ SY1580 )
| ~ ( ~ ( ( ( hAPP @ SY1582 @ SY1579 )
!= ( hAPP @ SY1582 @ SV235 ) )
| ( SY1579 = SV235 ) )
| ~ ( ( SY1579 != SV235 )
| ( ( hAPP @ SY1582 @ SY1579 )
= ( hAPP @ SY1582 @ SV235 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5935]) ).
thf(6182,plain,
! [SV236: $i] :
( ( ! [SY1585: $i,SY1586: $i,SY1587: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1587 @ tc_HOL_Obool ) ) @ SY1586 ) @ SY1585 ) @ SV236 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY1586 @ SV236 ) )
| ~ ( hBOOL @ ( hAPP @ SY1585 @ SV236 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5936]) ).
thf(6183,plain,
! [SV237: $i] :
( ( ! [SY1588: $i,SY1589: $i] :
( ~ ( c_Predicate_Oreflp @ SY1589 @ SY1588 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1588 @ SV237 ) @ SV237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5937]) ).
thf(6184,plain,
! [SV238: $i] :
( ( ! [SY1590: $i,SY1591: $i,SY1592: $i,SY1593: $i,SY1594: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1594 @ SY1593 @ SY1592 @ SY1591 @ SY1590 )
| ( ( hAPP @ SY1591 @ ( hAPP @ SY1592 @ SV238 ) )
= SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5938]) ).
thf(6185,plain,
! [SV239: $i] :
( ( ! [SY1595: $i] :
( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SY1595 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SY1595 @ ( c_Hilbert__Choice_OEps @ SV239 @ SY1595 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5939]) ).
thf(6186,plain,
! [SV240: $i] :
( ( ! [SY1597: $i,SY1598: $i,SY1599: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1599 @ tc_HOL_Obool ) ) @ SY1598 ) @ SY1597 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1599 @ tc_HOL_Obool ) ) @ SY1598 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1599 ) @ SV240 ) @ SY1597 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5940]) ).
thf(6187,plain,
! [SV241: $i] :
( ( ! [SY1600: $i,SY1601: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1601 @ tc_HOL_Obool ) ) @ SY1600 ) @ SV241 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1601 @ tc_HOL_Obool ) ) @ SV241 ) @ SY1600 ) )
| ( SY1600 = SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5941]) ).
thf(6188,plain,
! [SV242: $i] :
( ( ! [SY1602: $i,SY1603: $i] :
( ~ ( c_Wellfounded_OwfP @ SY1603 @ SY1602 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1603 @ ( tc_fun @ SY1603 @ tc_HOL_Obool ) ) ) @ SV242 ) @ SY1602 ) )
| ( c_Wellfounded_OwfP @ SY1603 @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5942]) ).
thf(6189,plain,
! [SV243: $i] :
( ( ! [SY1604: $i,SY1605: $i] :
( ~ ( class_Orderings_Oorder @ SY1605 )
| ~ ( ~ ( ( SY1604 != SV243 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1605 ) @ SY1604 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1605 ) @ SV243 ) @ SY1604 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1605 ) @ SY1604 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1605 ) @ SV243 ) @ SY1604 ) ) )
| ( SY1604 = SV243 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5943]) ).
thf(6190,plain,
! [SV244: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SV244 )
!= SV244 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5944]) ).
thf(6191,plain,
! [SV1: $i,SV245: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV245 @ tc_HOL_Obool ) ) @ SV1 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5945]) ).
thf(6192,plain,
! [SV2: $i,SV246: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV246 @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV246 @ tc_HOL_Obool ) ) ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5946]) ).
thf(6193,plain,
! [SV3: $i,SV247: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV247 @ tc_HOL_Obool ) ) @ SV3 ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV247 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5947]) ).
thf(6194,plain,
! [SV4: $i,SV248: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV248 @ SV4 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV248 ) @ tc_HOL_Obool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5948]) ).
thf(6195,plain,
! [SV5: $i,SV249: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV249 @ SV5 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV249 ) @ tc_HOL_Obool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5949]) ).
thf(6196,plain,
! [SV6: $i,SV250: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV250 @ tc_HOL_Obool ) ) @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5950]) ).
thf(6197,plain,
! [SV7: $i,SV251: $i] :
( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV251 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV251 @ tc_HOL_Obool ) ) @ SV7 ) )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5951]) ).
thf(6198,plain,
! [SV8: $i,SV252: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV252 @ tc_HOL_Obool ) ) @ SV8 ) @ SV8 )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5952]) ).
thf(6199,plain,
! [SV9: $i,SV253: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV253 @ tc_HOL_Obool ) ) @ SV9 ) @ SV9 )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5953]) ).
thf(6200,plain,
! [SV10: $i,SV254: $i] :
( ( ! [SY1606: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1606 @ tc_HOL_Obool ) ) @ SV254 ) @ SV10 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1606 @ tc_HOL_Obool ) ) @ SV10 ) @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5954]) ).
thf(6201,plain,
! [SV11: $i,SV255: $i] :
( ( ! [SY1607: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1607 @ tc_HOL_Obool ) ) @ SV255 ) @ SV11 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1607 @ tc_HOL_Obool ) ) @ SV11 ) @ SV255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5955]) ).
thf(6202,plain,
! [SV12: $i,SV256: $i] :
( ( ! [SY1608: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1608 @ tc_HOL_Obool ) ) @ SV256 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1608 @ tc_HOL_Obool ) ) @ SV256 ) @ SV12 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1608 @ tc_HOL_Obool ) ) @ SV256 ) @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5956]) ).
thf(6203,plain,
! [SV13: $i,SV257: $i] :
( ( ! [SY1609: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1609 @ tc_HOL_Obool ) ) @ SV257 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1609 @ tc_HOL_Obool ) ) @ SV257 ) @ SV13 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1609 @ tc_HOL_Obool ) ) @ SV257 ) @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5957]) ).
thf(6204,plain,
! [SV14: $i,SV258: $i] :
( ( ! [SY1610: $i,SY1611: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1611 @ tc_HOL_Obool ) ) @ SY1610 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1611 @ tc_HOL_Obool ) ) @ SV258 ) @ SV14 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1611 @ tc_HOL_Obool ) ) @ SV258 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1611 @ tc_HOL_Obool ) ) @ SY1610 ) @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5958]) ).
thf(6205,plain,
! [SV15: $i,SV259: $i] :
( ( ! [SY1612: $i,SY1613: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1613 @ tc_HOL_Obool ) ) @ SY1612 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1613 @ tc_HOL_Obool ) ) @ SV259 ) @ SV15 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1613 @ tc_HOL_Obool ) ) @ SV259 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1613 @ tc_HOL_Obool ) ) @ SY1612 ) @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5959]) ).
thf(6206,plain,
! [SV16: $i,SV260: $i] :
( ( ! [SY1614: $i,SY1615: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1615 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1615 @ tc_HOL_Obool ) ) @ SY1614 ) @ SV260 ) ) @ SV16 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1615 @ tc_HOL_Obool ) ) @ SY1614 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1615 @ tc_HOL_Obool ) ) @ SV260 ) @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5960]) ).
thf(6207,plain,
! [SV17: $i,SV261: $i] :
( ( ! [SY1616: $i,SY1617: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1617 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1617 @ tc_HOL_Obool ) ) @ SY1616 ) @ SV261 ) ) @ SV17 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1617 @ tc_HOL_Obool ) ) @ SY1616 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1617 @ tc_HOL_Obool ) ) @ SV261 ) @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5961]) ).
thf(6208,plain,
! [SV18: $i,SV262: $i] :
( ( ! [SY1618: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1618 @ tc_HOL_Obool ) ) @ SV262 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1618 @ tc_HOL_Obool ) ) @ SV262 ) @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5962]) ).
thf(6209,plain,
! [SV19: $i,SV263: $i] :
( ( ! [SY1619: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1619 @ tc_HOL_Obool ) ) @ SV263 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1619 @ tc_HOL_Obool ) ) @ SV19 ) @ SV263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5963]) ).
thf(6210,plain,
! [SV20: $i,SV264: $i] :
( ( ! [SY1620: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1620 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1620 @ tc_HOL_Obool ) ) @ SV264 ) @ SV20 ) ) @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5964]) ).
thf(6211,plain,
! [SV21: $i,SV265: $i] :
( ( ! [SY1621: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1621 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1621 @ tc_HOL_Obool ) ) @ SV265 ) @ SV21 ) ) @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5965]) ).
thf(6212,plain,
! [SV22: $i,SV266: $i] :
( ( ! [SY1622: $i,SY1623: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1623 ) @ SY1622 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1623 ) @ SV266 ) @ SV22 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1623 ) @ SV266 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1623 ) @ SY1622 ) @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5966]) ).
thf(6213,plain,
! [SV23: $i,SV267: $i] :
( ( ! [SY1624: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1624 ) @ SV267 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1624 ) @ SV267 ) @ SV23 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1624 ) @ SV267 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5967]) ).
thf(6214,plain,
! [SV24: $i,SV268: $i] :
( ( ! [SY1625: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1625 @ tc_HOL_Obool ) ) @ SV268 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1625 ) @ SV24 ) @ SV268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5968]) ).
thf(6215,plain,
! [SV25: $i,SV269: $i] :
( ( ! [SY1626: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1626 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1626 @ tc_HOL_Obool ) ) @ SV269 ) @ SV25 ) ) @ SV25 )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1626 @ tc_HOL_Obool ) ) @ SV269 ) @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5969]) ).
thf(6216,plain,
! [SV26: $i,SV270: $i] :
( ( ! [SY1627: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1627 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1627 @ tc_HOL_Obool ) ) @ SV270 ) @ SV26 ) ) @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5970]) ).
thf(6217,plain,
! [SV27: $i,SV271: $i] :
( ( ! [SY1628: $i,SY1629: $i] :
( ( c_Fun_Ofun__upd @ SY1629 @ SY1628 @ SV271 @ SV27 @ ( hAPP @ SV271 @ SV27 ) )
= SV271 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5971]) ).
thf(6218,plain,
! [SV28: $i,SV272: $i] :
( ( ! [SY1630: $i,SY1631: $i,SY1632: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SY1632 @ SY1631 @ SY1630 @ SV272 @ SV28 ) @ SV272 )
= SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5972]) ).
thf(6219,plain,
! [SV30: $i,SV273: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV273 ) @ SV30 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV30 ) @ SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5974]) ).
thf(6220,plain,
! [SV32: $i,SV274: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV274 ) @ SV32 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV32 ) @ SV274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5976]) ).
thf(6221,plain,
! [SV33: $i,SV275: $i] :
( ( ! [SY1633: $i,SY1634: $i,SY1635: $i,SY1636: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1636 @ SY1635 @ SY1634 @ SY1633 ) @ SV275 ) @ SV33 )
= ( hAPP @ SY1633 @ ( hAPP @ SV275 @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5977]) ).
thf(6222,plain,
! [SV34: $i,SV276: $i] :
( ( ! [SY1637: $i,SY1638: $i,SY1639: $i,SY1640: $i,SY1641: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY1641 @ SY1640 @ SY1639 @ SY1638 ) @ ( hAPP @ ( c_Fun_Ocomp @ SY1637 @ SY1641 @ SY1639 @ SV276 ) @ SV34 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SY1637 @ SY1640 @ SY1639 @ ( hAPP @ ( c_Fun_Ocomp @ SY1641 @ SY1640 @ SY1637 @ SY1638 ) @ SV276 ) ) @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5978]) ).
thf(6223,plain,
! [SV35: $i,SV277: $i] :
( ( ! [SY1642: $i,SY1643: $i,SY1644: $i,SY1645: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1645 @ SY1644 @ SY1643 @ SY1642 ) @ SV277 ) @ SV35 )
= ( hAPP @ SY1642 @ ( hAPP @ SV277 @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5979]) ).
thf(6224,plain,
! [SV36: $i,SV278: $i] :
( ( ! [SY1646: $i,SY1647: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1647 @ ( tc_fun @ SY1646 @ tc_HOL_Obool ) ) ) @ SV278 ) @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5980]) ).
thf(6225,plain,
! [SV37: $i,SV279: $i] :
( ( ( hAPP @ ( c_Set_OCollect @ SV279 ) @ SV37 )
= SV37 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5981]) ).
thf(6226,plain,
! [SV38: $i,SV280: $i] :
( ( ( hAPP @ ( c_Fun_Oid @ SV280 ) @ SV38 )
= SV38 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5982]) ).
thf(6227,plain,
! [SV39: $i,SV281: $i] :
( ( ( hAPP @ ( c_Fun_Oid @ SV281 ) @ SV39 )
= SV39 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5983]) ).
thf(6228,plain,
! [SV40: $i,SV282: $i] :
( ( ! [SY1648: $i,SY1649: $i,SY1650: $i,SY1651: $i,SY1652: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1652 @ SY1651 @ SY1650 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1652 @ SY1649 @ SY1651 ) @ SY1648 ) @ SV282 ) ) @ SV40 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1652 @ SY1649 @ SY1650 ) @ SY1648 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1649 @ SY1651 @ SY1650 ) @ SV282 ) @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5984]) ).
thf(6229,plain,
! [SV41: $i,SV283: $i] :
( ( ! [SY1653: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SY1653 @ SV283 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV283 @ SY1653 ) @ SV41 ) )
= SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5985]) ).
thf(6230,plain,
! [SV42: $i,SV284: $i] :
( ( ! [SY1654: $i,SY1655: $i] :
( ( hAPP @ SY1655 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY1654 @ SY1654 ) @ SV284 ) @ SY1655 ) @ SV42 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY1654 @ SY1654 ) @ SV284 ) @ SY1655 ) @ ( hAPP @ SY1655 @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5986]) ).
thf(6231,plain,
! [SV43: $i,SV285: $i] :
( ( ! [SY1656: $i,SY1657: $i,SY1658: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1658 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1658 @ SY1657 ) @ SY1656 ) @ SV285 ) ) @ SY1656 ) @ SV43 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1658 @ SY1657 ) @ SY1656 ) @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5987]) ).
thf(6232,plain,
! [SV44: $i,SV286: $i] :
( ( ! [SY1659: $i,SY1660: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1660 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1660 ) @ SY1659 ) @ SV286 ) ) @ SV44 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1660 ) @ SY1659 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1660 ) @ SV286 ) @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5988]) ).
thf(6233,plain,
! [SV45: $i,SV287: $i] :
( ( ( hAPP @ ( c_List_Orev @ SV287 ) @ ( hAPP @ ( c_List_Orev @ SV287 ) @ SV45 ) )
= SV45 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5989]) ).
thf(6234,plain,
! [SV47: $i,SV288: $i] :
( ( ( hAPP @ ( c_COMBI @ SV288 ) @ SV47 )
= SV47 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5991]) ).
thf(6235,plain,
! [SV48: $i,SV289: $i] :
( ( ! [SY1661: $i,SY1662: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ SY1662 @ SY1661 ) @ SV289 ) @ SV48 )
= SV289 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5992]) ).
thf(6236,plain,
! [SV49: $i,SV290: $i] :
( ( ! [SY1663: $i,SY1664: $i,SY1665: $i,SY1666: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1666 @ SY1665 @ SY1664 ) @ SY1663 ) @ SV290 ) @ SV49 )
= ( hAPP @ SY1663 @ ( hAPP @ SV290 @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5993]) ).
thf(6237,plain,
! [SV50: $i,SV291: $i] :
( ( ! [SY1667: $i,SY1668: $i,SY1669: $i,SY1670: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1670 @ SY1669 @ SY1668 ) @ SY1667 ) @ SV291 ) @ SV50 )
= ( hAPP @ ( hAPP @ SY1667 @ SV50 ) @ SV291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5994]) ).
thf(6238,plain,
! [SV51: $i,SV292: $i] :
( ( ! [SY1671: $i,SY1672: $i,SY1673: $i,SY1674: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1674 @ SY1673 @ SY1672 ) @ SY1671 ) @ SV292 ) @ SV51 )
= ( hAPP @ ( hAPP @ SY1671 @ SV51 ) @ ( hAPP @ SV292 @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5995]) ).
thf(6239,plain,
! [SV52: $i,SV293: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV293 ) @ SV52 ) )
| ( SV293 = SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5996]) ).
thf(6240,plain,
! [SV53: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_fNot @ SV53 ) ) )
= $true )
| ( ( ~ ( hBOOL @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5998]) ).
thf(6241,plain,
! [SV54: $i] :
( ( ( ~ ~ ( hBOOL @ SV54 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_fNot @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5999]) ).
thf(6242,plain,
! [SV55: $i,SV294: $i] :
( ( ~ ( hBOOL @ SV294 )
| ~ ( hBOOL @ SV55 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV294 ) @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6000]) ).
thf(6243,plain,
! [SV56: $i,SV295: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV295 ) @ SV56 ) )
| ( hBOOL @ SV295 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6001]) ).
thf(6244,plain,
! [SV57: $i,SV296: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV296 ) @ SV57 ) )
| ( hBOOL @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6002]) ).
thf(6245,plain,
! [SV58: $i,SV297: $i] :
( ( ~ ( hBOOL @ SV297 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV297 ) @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6003]) ).
thf(6246,plain,
! [SV59: $i,SV298: $i] :
( ( ~ ( hBOOL @ SV298 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV59 ) @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6004]) ).
thf(6247,plain,
! [SV60: $i,SV299: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV299 ) @ SV60 ) )
| ( hBOOL @ SV299 )
| ( hBOOL @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6005]) ).
thf(6248,plain,
! [SV61: $i,SV300: $i] :
( ( ( hBOOL @ SV300 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV300 ) @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6006]) ).
thf(6249,plain,
! [SV62: $i,SV301: $i] :
( ( ~ ( hBOOL @ SV301 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV62 ) @ SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6007]) ).
thf(6250,plain,
! [SV63: $i,SV302: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV302 ) @ SV63 ) )
| ~ ( hBOOL @ SV302 )
| ( hBOOL @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6008]) ).
thf(6251,plain,
! [SV64: $i,SV303: $i] :
( ( ! [SY1675: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1675 @ tc_HOL_Obool ) ) @ SV303 ) @ SV64 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1675 @ tc_HOL_Obool ) ) @ SV64 ) @ SV303 )
= SV303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6010]) ).
thf(6252,plain,
! [SV65: $i,SV304: $i] :
( ( ! [SY1676: $i,SY1677: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1677 @ SY1676 ) )
| ~ ( hBOOL @ ( hAPP @ SV304 @ SY1676 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV65 @ tc_HOL_Obool ) ) @ SY1677 ) @ SV304 ) @ SY1676 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6011]) ).
thf(6253,plain,
! [SV66: $i,SV305: $i] :
( ( ! [SY1678: $i,SY1679: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1679 @ tc_HOL_Obool ) ) @ SY1678 ) @ SV305 ) @ SV66 ) )
| ( hBOOL @ ( hAPP @ SY1678 @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6012]) ).
thf(6254,plain,
! [SV67: $i,SV306: $i] :
( ( ! [SY1680: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1680 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1680 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 )
= SV67 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1680 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 )
!= SV67 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1680 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6013]) ).
thf(6255,plain,
! [SV68: $i,SV307: $i] :
( ( ! [SY1681: $i] :
( ~ ( class_Orderings_Olinorder @ SY1681 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1681 ) @ SV307 ) @ SV68 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1681 ) @ SV68 ) @ SV307 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6014]) ).
thf(6256,plain,
! [SV69: $i,SV308: $i] :
( ( ! [SY1682: $i,SY1683: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1683 @ SY1682 @ SV308 ) @ SV69 ) )
| ~ ! [SY1684: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ SY1684 ) @ SV69 ) ) )
| ~ ( ~ ~ ! [SY1685: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ SY1685 ) @ SV69 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1683 @ SY1682 @ SV308 ) @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6015]) ).
thf(6257,plain,
! [SV70: $i,SV309: $i] :
( ( ~ ( ~ ( ~ ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
| ~ ( ~ ~ ! [SY1062: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1062 ) @ SY1062 ) )
| ~ ! [SY1063: $i,SY1064: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1064 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1064 ) @ SY1064 ) ) )
| ( ( hAPP @ SV70 @ SY1063 )
!= ( hAPP @ SV70 @ SY1064 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1064 ) @ SY1064 ) ) )
| ( ( hAPP @ SV70 @ SY1063 )
!= ( hAPP @ SV70 @ SY1064 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1064 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ! [SY1065: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1065 ) @ SY1065 ) )
| ~ ! [SY1066: $i,SY1067: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) ) ) ) )
| ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6016]) ).
thf(6258,plain,
! [SV71: $i,SV310: $i] :
( ( ! [SY1692: $i,SY1693: $i] :
( ( SY1693 != SY1692 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SY1693 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SY1692 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SY1692 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SY1693 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6017]) ).
thf(6259,plain,
! [SV72: $i,SV311: $i] :
( ( ~ ( class_Orderings_Otop @ SV311 )
| ( class_Orderings_Otop @ ( tc_fun @ SV72 @ SV311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6018]) ).
thf(6260,plain,
! [SV73: $i,SV312: $i] :
( ( ! [SY1694: $i,SY1695: $i,SY1696: $i,SY1697: $i,SY1698: $i,SY1699: $i,SY1700: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1700 @ SY1699 @ SY1698 @ SY1697 ) @ SY1696 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY1695 @ SY1699 @ SY1698 @ SY1694 ) @ SV312 ) )
| ( ( hAPP @ SY1697 @ ( hAPP @ SY1696 @ SV73 ) )
= ( hAPP @ SY1694 @ ( hAPP @ SV312 @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6019]) ).
thf(6261,plain,
! [SV74: $i,SV313: $i] :
( ( ! [SY1701: $i,SY1702: $i] :
( ~ ( class_Orderings_Oord @ SY1702 )
| ~ ! [SY1703: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1702 ) @ ( hAPP @ SY1701 @ SY1703 ) ) @ ( hAPP @ SV313 @ SY1703 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV74 @ SY1702 ) ) @ SY1701 ) @ SV313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6020]) ).
thf(6262,plain,
! [SV75: $i,SV314: $i] :
( ( ! [SY1704: $i,SY1705: $i,SY1706: $i,SY1707: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1707 @ SY1706 ) @ SY1705 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1704 @ SY1706 ) @ SY1705 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV314 @ ( tc_fun @ SV75 @ tc_HOL_Obool ) ) ) @ SY1707 ) @ SY1704 ) @ SY1706 ) @ SY1705 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6021]) ).
thf(6263,plain,
! [SV76: $i] :
( ( SV76
= ( hAPP @ c_Nat_OSuc @ SV76 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6022]) ).
thf(6264,plain,
! [SV77: $i,SV315: $i] :
( ( ! [SY1708: $i] :
( ( SY1708 != SV315 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV77 @ tc_HOL_Obool ) ) @ SY1708 ) @ SV315 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV77 @ tc_HOL_Obool ) ) @ SV315 ) @ SY1708 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6023]) ).
thf(6265,plain,
! [SV78: $i,SV316: $i] :
( ( ! [SY1709: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1709 @ tc_HOL_Obool ) ) @ SV316 ) @ SV78 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SY1709 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ SY1709 @ SV316 ) ) @ ( c_Predicate_OPowp @ SY1709 @ SV78 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6024]) ).
thf(6266,plain,
! [SV79: $i,SV317: $i] :
( ( ( SV317 != SV79 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV317 ) @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6025]) ).
thf(6267,plain,
! [SV80: $i,SV318: $i] :
( ( ! [SY1710: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY1710 @ SV318 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV318 @ SV80 ) @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6026]) ).
thf(6268,plain,
! [SV81: $i,SV319: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV319 )
| ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV81 @ SV319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6027]) ).
thf(6269,plain,
! [SV82: $i,SV320: $i] :
( ( ! [SY1711: $i,SY1712: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SY1712 @ SY1711 @ SV320 )
| ( ( hAPP @ ( hAPP @ SY1711 @ SV82 ) @ SV82 )
= SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6028]) ).
thf(6270,plain,
! [SV83: $i,SV321: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV321 )
!= ( hAPP @ c_Nat_OSuc @ SV83 ) )
| ( SV321 = SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6029]) ).
thf(6271,plain,
! [SV84: $i,SV322: $i] :
( ( ! [SY1713: $i,SY1714: $i,SY1715: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1715 @ tc_HOL_Obool ) ) @ SY1714 ) @ SY1713 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV322 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV322 @ SY1715 @ SV84 ) @ SY1714 ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV322 @ SY1715 @ SV84 ) @ SY1713 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6030]) ).
thf(6272,plain,
! [SV85: $i,SV323: $i] :
( ( ! [SY1716: $i] :
( ~ ~ ! [SX3: $i] :
~ ( hBOOL @ ( hAPP @ SY1716 @ SX3 ) )
| ( SV323
!= ( c_Hilbert__Choice_OEps @ SV85 @ SY1716 ) )
| ( hBOOL @ ( hAPP @ SY1716 @ SV323 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6031]) ).
thf(6273,plain,
! [SV86: $i,SV324: $i] :
( ( ! [SY1718: $i,SY1719: $i] :
( ( SY1719 != SY1718 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SY1719 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SY1718 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SY1719 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SY1718 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6032]) ).
thf(6274,plain,
! [SV87: $i,SV325: $i] :
( ( ! [SY1720: $i,SY1721: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1721 @ tc_HOL_Obool ) ) @ SY1720 ) @ SV325 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1721 @ tc_HOL_Obool ) ) @ SV325 ) @ SV87 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1721 @ tc_HOL_Obool ) ) @ SY1720 ) @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6033]) ).
thf(6275,plain,
! [SV88: $i,SV326: $i] :
( ( ! [SY1722: $i,SY1723: $i,SY1724: $i,SY1725: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1725 @ ( tc_fun @ SY1724 @ tc_HOL_Obool ) ) ) @ SY1723 ) @ SY1722 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1723 @ SV326 ) @ SV88 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1722 @ SV326 ) @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6034]) ).
thf(6276,plain,
! [SV89: $i,SV327: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV327 )
!= ( hAPP @ c_Int_ORep__Integ @ SV89 ) )
| ( SV327 = SV89 ) )
| ~ ( ( SV327 != SV89 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV327 )
= ( hAPP @ c_Int_ORep__Integ @ SV89 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6035]) ).
thf(6277,plain,
! [SV90: $i,SV328: $i] :
( ( ! [SY1726: $i,SY1727: $i,SY1728: $i,SY1729: $i] :
( ~ ( ( SY1729 != SY1728 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1727 @ SY1726 @ SV328 @ SY1728 @ SV90 ) @ SY1729 )
= ( hAPP @ SV328 @ SY1729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6036]) ).
thf(6278,plain,
! [SV91: $i,SV329: $i] :
( ( ! [SY1730: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY1730 ) @ SV329 )
!= ( hAPP @ ( c_List_Orev @ SY1730 ) @ SV91 ) )
| ( SV329 = SV91 ) )
| ~ ( ( SV329 != SV91 )
| ( ( hAPP @ ( c_List_Orev @ SY1730 ) @ SV329 )
= ( hAPP @ ( c_List_Orev @ SY1730 ) @ SV91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6037]) ).
thf(6279,plain,
! [SV92: $i,SV330: $i] :
( ( ! [SY1731: $i,SY1732: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1732 @ SY1731 @ SV330 ) @ SV92 ) )
| ~ ! [SY1733: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ SY1733 ) ) )
| ~ ( ~ ~ ! [SY1734: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ SY1734 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1732 @ SY1731 @ SV330 ) @ SV92 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6038]) ).
thf(6280,plain,
! [SV93: $i,SV331: $i] :
( ( ! [SY1735: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1735 ) @ tc_HOL_Obool ) ) @ SV331 ) @ SV93 ) )
| ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1735 @ SV93 @ SV331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6039]) ).
thf(6281,plain,
! [SV94: $i,SV332: $i] :
( ( ~ ( class_Groups_Ouminus @ SV332 )
| ( class_Groups_Ouminus @ ( tc_fun @ SV94 @ SV332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6040]) ).
thf(6282,plain,
! [SV95: $i,SV333: $i] :
( ( ! [SY1736: $i,SY1737: $i,SY1738: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1738 @ tc_HOL_Obool ) ) @ SY1737 ) @ SY1736 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1738 @ tc_HOL_Obool ) ) @ SV333 ) @ SV95 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1738 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1738 @ tc_HOL_Obool ) ) @ SY1737 ) @ SV333 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1738 @ tc_HOL_Obool ) ) @ SY1736 ) @ SV95 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6041]) ).
thf(6283,plain,
! [SV96: $i,SV334: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV334 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV96 ) )
| ( SV334 = SV96 ) )
| ~ ( ( SV334 != SV96 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV334 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV96 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6042]) ).
thf(6284,plain,
! [SV97: $i,SV335: $i] :
( ( ! [SY1739: $i,SY1740: $i,SY1741: $i,SY1742: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1742 @ ( tc_fun @ SY1741 @ tc_HOL_Obool ) ) ) @ SY1740 ) @ SY1739 ) @ SV335 ) @ SV97 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1740 @ SV335 ) @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6043]) ).
thf(6285,plain,
! [SV98: $i,SV336: $i] :
( ( ! [SY1743: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1743 @ tc_HOL_Obool ) ) @ SV336 ) @ SV98 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1743 @ tc_HOL_Obool ) ) @ SV336 ) @ SV98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6044]) ).
thf(6286,plain,
! [SV99: $i,SV337: $i] :
( ( ! [SY1744: $i,SY1745: $i,SY1746: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1746 @ SY1745 @ SY1744 ) @ SV337 ) @ SV99 ) )
| ( hBOOL @ ( hAPP @ SV337 @ ( hAPP @ SY1744 @ SV99 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV337 @ ( hAPP @ SY1744 @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1746 @ SY1745 @ SY1744 ) @ SV337 ) @ SV99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6045]) ).
thf(6287,plain,
! [SV100: $i,SV338: $i] :
( ( ! [SY1747: $i,SY1748: $i,SY1749: $i,SY1750: $i,SY1751: $i,SY1752: $i,SY1753: $i,SY1754: $i,SY1755: $i] :
( ( ( hAPP @ SY1755 @ ( hAPP @ SY1754 @ SY1753 ) )
!= ( hAPP @ SY1752 @ ( hAPP @ SY1751 @ SY1750 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1749 @ SY1748 @ SY1747 @ SY1755 ) @ SY1754 ) @ SY1753 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV338 @ SY1748 @ SV100 @ SY1752 ) @ SY1751 ) @ SY1750 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6046]) ).
thf(6288,plain,
! [SV101: $i,SV339: $i] :
( ( ! [SY1756: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1756 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1756 @ tc_HOL_Obool ) ) @ SV339 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1756 @ tc_HOL_Obool ) ) @ SV101 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1756 @ tc_HOL_Obool ) ) @ SV101 ) @ SV339 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1756 @ tc_HOL_Obool ) ) @ SV101 ) @ SV339 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1756 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1756 @ tc_HOL_Obool ) ) @ SV339 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1756 @ tc_HOL_Obool ) ) @ SV101 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6047]) ).
thf(6289,plain,
! [SV102: $i,SV340: $i] :
( ( ! [SY1757: $i,SY1758: $i,SY1759: $i,SY1760: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY1760 @ SY1759 @ SY1758 )
| ( ( hAPP @ ( hAPP @ SY1758 @ SY1757 ) @ ( hAPP @ ( hAPP @ SY1758 @ SV340 ) @ SV102 ) )
= ( hAPP @ ( hAPP @ SY1758 @ SV340 ) @ ( hAPP @ ( hAPP @ SY1758 @ SY1757 ) @ SV102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6048]) ).
thf(6290,plain,
! [SV103: $i,SV341: $i] :
( ( ! [SY1761: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1761 @ SV341 ) @ SV103 ) )
| ! [SY1762: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SY1762 ) @ SV103 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1761 @ SV341 ) @ SY1762 ) ) ) )
| ~ ( ~ ! [SY1763: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SY1763 ) @ SV103 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1761 @ SV341 ) @ SY1763 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1761 @ SV341 ) @ SV103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6049]) ).
thf(6291,plain,
! [SV104: $i,SV342: $i] :
( ( ! [SY1764: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1764 @ tc_HOL_Obool ) ) @ SV342 ) @ SV104 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1764 @ tc_HOL_Obool ) ) @ SV342 ) @ SV104 )
= SV342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6050]) ).
thf(6292,plain,
! [SV105: $i,SV343: $i] :
( ( ! [SY1765: $i,SY1766: $i,SY1767: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SY1767 @ SY1766 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1766 @ SY1765 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1766 @ SV343 ) @ SV105 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1766 @ SY1765 ) @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6051]) ).
thf(6293,plain,
! [SV106: $i,SV344: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV344 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV344 ) @ SV106 ) @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6052]) ).
thf(6294,plain,
! [SV107: $i,SV345: $i] :
( ( ~ ( class_Lattices_Olattice @ SV345 )
| ( class_Lattices_Olattice @ ( tc_fun @ SV107 @ SV345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6053]) ).
thf(6295,plain,
! [SV108: $i,SV346: $i] :
( ( ~ ~ ! [SY1768: $i] :
~ ( hBOOL @ ( hAPP @ SV346 @ SY1768 ) )
| ( hBOOL @ ( hAPP @ SV346 @ ( c_Hilbert__Choice_OEps @ SV108 @ SV346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6054]) ).
thf(6296,plain,
! [SV109: $i,SV347: $i] :
( ( ! [SY1769: $i,SY1770: $i,SY1771: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1771 @ SY1770 ) @ SY1769 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV347 @ SV109 @ SY1771 ) @ SY1769 ) @ SY1770 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6055]) ).
thf(6297,plain,
! [SV110: $i,SV348: $i] :
( ( ! [SY1772: $i,SY1773: $i,SY1774: $i] :
~ ( ~ ( ( ( c_Fun_Ofun__upd @ SY1774 @ SY1773 @ SY1772 @ SV348 @ SV110 )
!= SY1772 )
| ( ( hAPP @ SY1772 @ SV348 )
= SV110 ) )
| ~ ( ( ( hAPP @ SY1772 @ SV348 )
!= SV110 )
| ( ( c_Fun_Ofun__upd @ SY1774 @ SY1773 @ SY1772 @ SV348 @ SV110 )
= SY1772 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6056]) ).
thf(6298,plain,
! [SV111: $i,SV349: $i] :
( ( ! [SY1775: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1775 @ tc_HOL_Obool ) ) @ SV349 ) @ SV111 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SY1775 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ SY1775 ) @ SV349 ) ) @ ( hAPP @ ( c_Set_OPow @ SY1775 ) @ SV111 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6057]) ).
thf(6299,plain,
! [SV112: $i,SV350: $i] :
( ( ! [SY1776: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1776 @ SV350 ) @ SV112 ) )
| ! [SY1777: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV350 @ SY1777 ) @ SV112 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1776 @ SV350 ) @ SY1777 ) ) ) )
| ~ ( ~ ! [SY1778: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV350 @ SY1778 ) @ SV112 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1776 @ SV350 ) @ SY1778 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1776 @ SV350 ) @ SV112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6058]) ).
thf(6300,plain,
! [SV113: $i,SV351: $i] :
( ( ! [SY1779: $i,SY1780: $i] :
( ~ ( c_Predicate_Osymp @ SY1780 @ SY1779 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1779 @ SV351 ) @ SV113 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1779 @ SV113 ) @ SV351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6059]) ).
thf(6301,plain,
! [SV114: $i,SV352: $i] :
( ( ! [SY1781: $i,SY1782: $i,SY1783: $i,SY1784: $i] :
~ ( ~ ( ( SY1784 != SY1783 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1782 @ SY1781 @ SV352 @ SY1783 @ SV114 ) @ SY1784 )
= SV114 ) )
| ~ ( ~ ( ( SY1784 != SY1783 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1782 @ SY1781 @ SV352 @ SY1783 @ SV114 ) @ SY1784 )
= ( hAPP @ SV352 @ SY1784 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6060]) ).
thf(6302,plain,
! [SV115: $i,SV353: $i] :
( ( ! [SY1785: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1785 @ tc_HOL_Obool ) ) @ SV353 ) @ SV115 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY1785 ) @ SV115 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY1785 ) @ SV353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6061]) ).
thf(6303,plain,
! [SV116: $i,SV354: $i] :
( ( ~ ~ ( ~ ( class_Enum_Oenum @ SV354 )
| ~ ( class_Enum_Oenum @ SV116 ) )
| ( class_Enum_Oenum @ ( tc_fun @ SV354 @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6062]) ).
thf(6304,plain,
! [SV117: $i,SV355: $i] :
( ( ! [SY1786: $i,SY1787: $i,SY1788: $i,SY1789: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1789 @ SY1788 ) @ SY1787 ) @ SY1786 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1789 @ SY1788 ) @ SV355 ) @ SV117 ) )
| ~ ( ( SY1787 != SV355 )
| ( SY1786 != SV117 ) ) )
| ~ ( ~ ~ ( ( SY1787 != SV355 )
| ( SY1786 != SV117 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1789 @ SY1788 ) @ SY1787 ) @ SY1786 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1789 @ SY1788 ) @ SV355 ) @ SV117 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6063]) ).
thf(6305,plain,
! [SV118: $i,SV356: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV356 ) @ SV118 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV118 ) @ SV356 ) )
| ( SV356 = SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6064]) ).
thf(6306,plain,
! [SV119: $i,SV357: $i] :
( ( ! [SY1790: $i,SY1791: $i,SY1792: $i,SY1793: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1793 @ ( tc_fun @ SY1792 @ tc_HOL_Obool ) ) ) @ SY1791 ) @ SY1790 ) @ SV357 ) @ SV119 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1790 @ SV357 ) @ SV119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6065]) ).
thf(6307,plain,
! [SV120: $i,SV358: $i] :
( ( ! [SY1794: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1794 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1794 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
| ( SV358 = SV120 ) )
| ~ ( ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1794 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
| ( SV358 = SV120 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1794 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6066]) ).
thf(6308,plain,
! [SV121: $i,SV359: $i] :
( ( ! [SY1795: $i,SY1796: $i] :
( ~ ( class_Orderings_Oord @ SY1796 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1795 @ SY1796 ) ) @ SV359 ) @ SV121 ) )
| ! [SY1797: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1796 ) @ ( hAPP @ SV359 @ SY1797 ) ) @ ( hAPP @ SV121 @ SY1797 ) ) ) )
| ~ ( ~ ! [SY1798: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1796 ) @ ( hAPP @ SV359 @ SY1798 ) ) @ ( hAPP @ SV121 @ SY1798 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1795 @ SY1796 ) ) @ SV359 ) @ SV121 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6067]) ).
thf(6309,plain,
! [SV122: $i,SV360: $i] :
( ( ! [SY1799: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1799 @ SV360 ) )
| ( hBOOL @ ( hAPP @ SY1799 @ ( c_Hilbert__Choice_OEps @ SV122 @ SY1799 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6068]) ).
thf(6310,plain,
! [SV123: $i,SV361: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV361 @ ( c_Hilbert__Choice_OEps @ SV123 @ SV361 ) ) )
| ~ ! [SY1800: $i] :
~ ( hBOOL @ ( hAPP @ SV361 @ SY1800 ) ) )
| ~ ( ~ ~ ! [SY1801: $i] :
~ ( hBOOL @ ( hAPP @ SV361 @ SY1801 ) )
| ( hBOOL @ ( hAPP @ SV361 @ ( c_Hilbert__Choice_OEps @ SV123 @ SV361 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6069]) ).
thf(6311,plain,
! [SV124: $i,SV362: $i] :
( ( ~ ! [SY1802: $i] :
( ( hAPP @ SV362 @ SY1802 )
= ( hAPP @ SV124 @ SY1802 ) )
| ( SV362 = SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6070]) ).
thf(6312,plain,
! [SV125: $i,SV363: $i] :
( ( ! [SY1803: $i,SY1804: $i,SY1805: $i] :
( ~ ( c_Fun_Oinj__on @ SY1805 @ SY1804 @ SY1803 @ SV363 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1805 @ tc_HOL_Obool ) ) @ SV125 ) @ SV363 ) )
| ( c_Fun_Oinj__on @ SY1805 @ SY1804 @ SY1803 @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6071]) ).
thf(6313,plain,
! [SV126: $i,SV364: $i] :
( ( ! [SY1806: $i,SY1807: $i] :
( ~ ( class_Orderings_Oord @ SY1807 )
| ( SY1806 != SV364 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1807 ) @ SV364 ) @ SV126 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1807 ) @ SY1806 ) @ SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6072]) ).
thf(6314,plain,
! [SV127: $i,SV365: $i] :
( ( ! [SY1808: $i,SY1809: $i,SY1810: $i,SY1811: $i,SY1812: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1812 @ SY1811 @ SY1810 @ SY1809 ) @ SY1808 )
!= SV365 )
| ( ( hAPP @ SY1809 @ ( hAPP @ SY1808 @ SV127 ) )
= ( hAPP @ SV365 @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6073]) ).
thf(6315,plain,
! [SV128: $i,SV366: $i] :
( ( ! [SY1813: $i,SY1814: $i,SY1815: $i,SY1816: $i] :
~ ( ~ ( ( SY1816 != SY1815 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1814 @ SY1813 @ SV366 @ SY1815 @ SV128 ) @ SY1816 )
= SV128 ) )
| ~ ( ~ ( ( SY1816 != SY1815 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1814 @ SY1813 @ SV366 @ SY1815 @ SV128 ) @ SY1816 )
= ( hAPP @ SV366 @ SY1816 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6074]) ).
thf(6316,plain,
! [SV129: $i,SV367: $i] :
( ( ! [SY1817: $i,SY1818: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1818 ) @ SY1817 ) @ SV367 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1818 ) @ SY1817 ) @ SV129 ) )
| ( SV367 = SV129 ) )
| ~ ( ( SV367 != SV129 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1818 ) @ SY1817 ) @ SV367 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1818 ) @ SY1817 ) @ SV129 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6075]) ).
thf(6317,plain,
! [SV130: $i,SV368: $i] :
( ( ! [SY1819: $i,SY1820: $i] :
( ~ ( class_Orderings_Opreorder @ SY1820 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1820 ) @ SY1819 ) @ SV368 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1820 ) @ SV368 ) @ SV130 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1820 ) @ SY1819 ) @ SV130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6076]) ).
thf(6318,plain,
! [SV131: $i,SV369: $i] :
( ( ! [SY1821: $i,SY1822: $i] :
( ( SY1822 != SY1821 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SY1822 ) @ SV131 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SY1821 ) @ SV131 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SY1821 ) @ SV131 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SY1822 ) @ SV131 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6077]) ).
thf(6319,plain,
! [SV132: $i,SV370: $i] :
( ( ! [SY1823: $i,SY1824: $i,SY1825: $i,SY1826: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1826 ) @ SY1825 ) @ SY1824 )
!= SY1823 )
| ( SV370
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1826 ) @ SY1824 ) @ SV132 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1826 ) @ SY1825 ) @ SV370 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1826 ) @ SY1823 ) @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6078]) ).
thf(6320,plain,
! [SV133: $i,SV371: $i] :
( ( ! [SY1827: $i,SY1828: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1828 ) @ SY1827 ) @ SV371 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1828 ) @ SV133 ) @ SV371 ) )
| ( SY1827 = SV133 ) )
| ~ ( ( SY1827 != SV133 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1828 ) @ SY1827 ) @ SV371 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1828 ) @ SV133 ) @ SV371 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6079]) ).
thf(6321,plain,
! [SV134: $i,SV372: $i] :
( ( ! [SY1829: $i,SY1830: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1830 @ tc_HOL_Obool ) ) @ SY1829 ) @ SV372 ) )
| ~ ( hBOOL @ ( hAPP @ SY1829 @ SV134 ) )
| ( hBOOL @ ( hAPP @ SV372 @ SV134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6080]) ).
thf(6322,plain,
! [SV135: $i,SV373: $i] :
( ( ! [SY1831: $i,SY1832: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SY1832 @ SY1831 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1831 @ SV373 ) @ SV135 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1831 @ SV135 ) @ SV373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6081]) ).
thf(6323,plain,
! [SV136: $i,SV374: $i] :
( ( ! [SY1833: $i,SY1834: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY1834 @ SY1833 ) @ SV374 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY1834 @ SY1833 ) @ SV136 ) )
| ( SV374 = SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6082]) ).
thf(6324,plain,
! [SV137: $i,SV375: $i] :
( ( ! [SY1835: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1835 ) @ SV375 ) @ SV137 ) )
| ( hBOOL @ ( hAPP @ SV137 @ SV375 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV137 @ SV375 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1835 ) @ SV375 ) @ SV137 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6083]) ).
thf(6325,plain,
! [SV138: $i,SV376: $i] :
( ( ! [SY1836: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1836 @ ( tc_fun @ SY1836 @ tc_HOL_Obool ) ) ) @ SV376 ) @ SV138 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1836 @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ SY1836 @ SV138 ) ) @ ( c_Wellfounded_Oaccp @ SY1836 @ SV376 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6084]) ).
thf(6326,plain,
! [SV139: $i,SV377: $i] :
( ( ! [SY1837: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1837 @ tc_HOL_Obool ) ) @ SV377 ) @ SV139 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1837 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1837 @ tc_HOL_Obool ) ) @ SV139 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1837 @ tc_HOL_Obool ) ) @ SV377 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6085]) ).
thf(6327,plain,
! [SV140: $i,SV378: $i] :
( ( ! [SY1838: $i,SY1839: $i,SY1840: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1840 @ SY1839 ) @ SY1838 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV378 @ SV140 @ SY1840 ) @ SY1838 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6086]) ).
thf(6328,plain,
! [SV141: $i,SV379: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV379 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV141 ) )
| ( SV379 = SV141 ) )
| ~ ( ( SV379 != SV141 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV379 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV141 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6087]) ).
thf(6329,plain,
! [SV142: $i,SV380: $i] :
( ( ! [SY1841: $i,SY1842: $i,SY1843: $i,SY1844: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1844 @ ( tc_fun @ SY1843 @ tc_HOL_Obool ) ) ) @ SY1842 ) @ SY1841 ) @ SV380 ) @ SV142 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1842 @ SV380 ) @ SV142 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1841 @ SV380 ) @ SV142 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6088]) ).
thf(6330,plain,
! [SV143: $i,SV381: $i] :
( ( ! [SY1845: $i,SY1846: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1846 @ tc_HOL_Obool ) ) @ SY1845 ) @ SV381 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1846 @ tc_HOL_Obool ) ) @ SY1845 ) @ SV143 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1846 @ tc_HOL_Obool ) ) @ SY1845 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1846 @ tc_HOL_Obool ) ) @ SV381 ) @ SV143 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6089]) ).
thf(6331,plain,
! [SV144: $i,SV382: $i] :
( ( ! [SY1847: $i] :
~ ( ~ ( ( SY1847 != SV382 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SY1847 ) @ SV382 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV382 ) @ SY1847 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SY1847 ) @ SV382 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV382 ) @ SY1847 ) ) )
| ( SY1847 = SV382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6090]) ).
thf(6332,plain,
! [SV145: $i,SV383: $i] :
( ( ! [SY1848: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SY1848 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SV383 ) @ SV145 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1848 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SY1848 @ tc_HOL_Obool ) @ SV145 ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SY1848 @ tc_HOL_Obool ) @ SV383 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6091]) ).
thf(6333,plain,
! [SV146: $i,SV384: $i] :
( ( ! [SY1849: $i,SY1850: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1850 @ SY1849 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV384 @ tc_HOL_Obool ) ) @ SY1850 ) @ SV146 ) )
| ( hBOOL @ ( hAPP @ SV146 @ SY1849 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6092]) ).
thf(6334,plain,
! [SV147: $i,SV385: $i] :
( ( ! [SY1851: $i,SY1852: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1852 @ tc_HOL_Obool ) ) @ SY1851 ) @ SV385 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1852 @ tc_HOL_Obool ) ) @ SV385 ) @ SV147 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1852 @ tc_HOL_Obool ) ) @ SY1851 ) @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6093]) ).
thf(6335,plain,
! [SV148: $i,SV386: $i] :
( ( ! [SY1853: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SY1853 ) @ SV386 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV386 ) @ SV148 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SY1853 ) @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6094]) ).
thf(6336,plain,
! [SV149: $i,SV387: $i] :
( ( ! [SY1854: $i,SY1855: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1855 @ SY1854 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV387 @ tc_HOL_Obool ) ) @ SY1855 ) @ SV149 ) @ SY1854 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6095]) ).
thf(6337,plain,
! [SV150: $i,SV388: $i] :
( ( ! [SY1856: $i,SY1857: $i,SY1858: $i] :
( ~ ( class_Orderings_Oord @ SY1858 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1857 @ SY1858 ) ) @ SY1856 ) @ SV388 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1858 ) @ ( hAPP @ SY1856 @ SV150 ) ) @ ( hAPP @ SV388 @ SV150 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6096]) ).
thf(6338,plain,
! [SV151: $i,SV389: $i] :
( ( ! [SY1859: $i,SY1860: $i,SY1861: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1861 @ SY1860 ) @ SY1859 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV389 @ SV151 @ SY1861 ) @ SY1860 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6097]) ).
thf(6339,plain,
! [SV152: $i,SV390: $i] :
( ( ! [SY1862: $i,SY1863: $i,SY1864: $i,SY1865: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1865 @ SY1864 ) @ SY1863 ) @ SY1862 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1865 @ SY1864 ) @ SV390 ) @ SV152 ) )
| ~ ( ( SY1863 != SV390 )
| ( SY1862 != SV152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6098]) ).
thf(6340,plain,
! [SV153: $i,SV391: $i] :
( ( ! [SY1866: $i,SY1867: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1867 @ tc_HOL_Obool ) ) @ SY1866 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1867 ) @ SV153 ) @ SY1866 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1867 ) @ SV153 ) @ SV391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6099]) ).
thf(6341,plain,
! [SV154: $i,SV392: $i] :
( ( ! [SY1868: $i,SY1869: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1869 @ tc_HOL_Obool ) ) @ SY1868 ) @ SV392 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1869 ) @ SV154 ) @ SY1868 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1869 ) @ SV154 ) @ SV392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6100]) ).
thf(6342,plain,
! [SV155: $i,SV393: $i] :
( ( ! [SY1870: $i,SY1871: $i,SY1872: $i,SY1873: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1873 @ SY1872 ) @ SY1871 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1870 @ SY1872 ) @ SY1871 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV393 @ ( tc_fun @ SV155 @ tc_HOL_Obool ) ) ) @ SY1870 ) @ SY1873 ) @ SY1872 ) @ SY1871 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6101]) ).
thf(6343,plain,
! [SV156: $i,SV394: $i] :
( ( ! [SY1874: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1874 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1874 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
| ~ ( ( SV394 != SV156 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1874 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
| ~ ( ( SV394 != SV156 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1874 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6102]) ).
thf(6344,plain,
! [SV157: $i,SV395: $i] :
( ( ! [SY1875: $i,SY1876: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1876 @ tc_HOL_Obool ) ) @ SY1875 ) @ SV395 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1876 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1876 ) @ SV157 ) @ SY1875 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1876 ) @ SV157 ) @ SV395 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6103]) ).
thf(6345,plain,
! [SV158: $i,SV396: $i] :
( ( ~ ( class_Orderings_Oord @ SV396 )
| ( class_Orderings_Oord @ ( tc_fun @ SV158 @ SV396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6104]) ).
thf(6346,plain,
! [SV159: $i,SV397: $i] :
( ( ! [SY1877: $i,SY1878: $i,SY1879: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1879 @ SY1878 @ SY1877 ) @ SV397 ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1877 @ SV159 ) @ SV397 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1877 @ SV159 ) @ SV397 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1879 @ SY1878 @ SY1877 ) @ SV397 ) @ SV159 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6105]) ).
thf(6347,plain,
! [SV160: $i,SV398: $i] :
( ( ! [SY1880: $i,SY1881: $i,SY1882: $i] :
( ~ ( c_Predicate_Otransp @ SY1882 @ SY1881 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1881 @ SY1880 ) @ SV398 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1881 @ SV398 ) @ SV160 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1881 @ SY1880 ) @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6106]) ).
thf(6348,plain,
! [SV161: $i,SV399: $i] :
( ( ! [SY1883: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1883 @ tc_HOL_Obool ) ) @ SV399 )
!= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1883 @ tc_HOL_Obool ) ) @ SV161 ) )
| ( SV399 = SV161 ) )
| ~ ( ( SV399 != SV161 )
| ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1883 @ tc_HOL_Obool ) ) @ SV399 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1883 @ tc_HOL_Obool ) ) @ SV161 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6107]) ).
thf(6349,plain,
! [SV162: $i,SV400: $i] :
( ( ! [SY1884: $i,SY1885: $i,SY1886: $i] :
( ~ ( class_Orderings_Oord @ SY1886 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1885 @ SY1886 ) ) @ SY1884 ) @ SV400 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1886 ) @ ( hAPP @ SY1884 @ SV162 ) ) @ ( hAPP @ SV400 @ SV162 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6108]) ).
thf(6350,plain,
! [SV163: $i,SV401: $i] :
( ( ! [SY1887: $i,SY1888: $i] :
( ~ ( class_Orderings_Oorder @ SY1888 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1888 ) @ SY1887 ) @ SV401 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1888 ) @ SV163 ) @ SY1887 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1888 ) @ SV163 ) @ SV401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6109]) ).
thf(6351,plain,
! [SV164: $i,SV402: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV402 )
!= ( hAPP @ c_Nat_OSuc @ SV164 ) )
| ( SV402 = SV164 ) )
| ~ ( ( SV402 != SV164 )
| ( ( hAPP @ c_Nat_OSuc @ SV402 )
= ( hAPP @ c_Nat_OSuc @ SV164 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6110]) ).
thf(6352,plain,
! [SV165: $i,SV403: $i] :
( ( ! [SY1889: $i,SY1890: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1890 @ SY1889 ) @ SV403 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1889 @ SV165 ) @ SV403 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1890 @ SY1889 ) @ SV165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6111]) ).
thf(6353,plain,
! [SV166: $i,SV404: $i] :
( ( ! [SY1891: $i,SY1892: $i] :
( ~ ( class_Orderings_Oord @ SY1892 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1892 ) @ SY1891 ) @ SV404 ) )
| ( SV404 != SV166 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1892 ) @ SY1891 ) @ SV166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6112]) ).
thf(6354,plain,
! [SV167: $i,SV405: $i] :
( ( ! [SY1893: $i,SY1894: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1894 @ tc_HOL_Obool ) ) @ SY1893 ) @ SV405 ) @ SV167 ) )
| ( hBOOL @ ( hAPP @ SV405 @ SV167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6113]) ).
thf(6355,plain,
! [SV168: $i,SV406: $i] :
( ( ! [SY1895: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1895 @ tc_HOL_Obool ) ) @ SV406 ) @ SV168 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1895 @ tc_HOL_Obool ) ) @ SV406 ) @ SV168 )
= SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6114]) ).
thf(6356,plain,
! [SV169: $i,SV407: $i] :
( ( ! [SY1896: $i,SY1897: $i,SY1898: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1898 @ tc_HOL_Obool ) ) @ SY1897 ) @ ( hAPP @ ( c_Set_Oimage @ SY1896 @ SY1898 @ SV407 ) @ SV169 ) ) )
| ~ ! [SY1899: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1896 @ tc_HOL_Obool ) ) @ SY1899 ) @ SV169 ) )
| ( SY1897
!= ( hAPP @ ( c_Set_Oimage @ SY1896 @ SY1898 @ SV407 ) @ SY1899 ) ) ) )
| ~ ( ~ ~ ! [SY1900: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1896 @ tc_HOL_Obool ) ) @ SY1900 ) @ SV169 ) )
| ( SY1897
!= ( hAPP @ ( c_Set_Oimage @ SY1896 @ SY1898 @ SV407 ) @ SY1900 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1898 @ tc_HOL_Obool ) ) @ SY1897 ) @ ( hAPP @ ( c_Set_Oimage @ SY1896 @ SY1898 @ SV407 ) @ SV169 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6115]) ).
thf(6357,plain,
! [SV170: $i,SV408: $i] :
( ( ! [SY1901: $i,SY1902: $i,SY1903: $i,SY1904: $i] :
( ( SY1904 != SY1903 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1902 @ SY1901 @ SV408 ) @ SV170 ) @ SY1904 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1902 @ SY1901 @ SV408 ) @ SV170 ) @ SY1903 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6116]) ).
thf(6358,plain,
! [SV171: $i,SV409: $i] :
( ( ! [SY1905: $i,SY1906: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1906 @ SY1905 ) )
| ( hBOOL @ ( hAPP @ SV409 @ SY1905 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV171 @ tc_HOL_Obool ) ) @ SV409 ) @ SY1906 ) @ SY1905 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6117]) ).
thf(6359,plain,
! [SV172: $i,SV410: $i] :
( ( ! [SY1907: $i,SY1908: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1908 @ tc_HOL_Obool ) ) @ SY1907 ) @ SV410 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1908 @ tc_HOL_Obool ) ) @ SV410 ) @ SV172 ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1908 @ tc_HOL_Obool ) ) @ SV410 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1908 @ tc_HOL_Obool ) ) @ SV172 ) @ SY1907 ) )
= SY1907 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6118]) ).
thf(6360,plain,
! [SV173: $i,SV411: $i] :
( ( ! [SY1909: $i] :
( ~ ( class_Orderings_Olinorder @ SY1909 )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1909 ) @ SV411 ) @ SV173 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1909 ) @ SV173 ) @ SV411 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6119]) ).
thf(6361,plain,
! [SV174: $i,SV412: $i] :
( ( ! [SY1910: $i,SY1911: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1911 @ SY1910 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV412 @ tc_HOL_Obool ) ) @ SV174 ) @ SY1911 ) @ SY1910 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6120]) ).
thf(6362,plain,
! [SV175: $i,SV413: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV413 )
| ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV175 @ SV413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6121]) ).
thf(6363,plain,
! [SV176: $i,SV414: $i] :
( ( ~ ( class_Groups_Ominus @ SV414 )
| ( class_Groups_Ominus @ ( tc_fun @ SV176 @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6122]) ).
thf(6364,plain,
! [SV177: $i,SV415: $i] :
( ( ! [SY1912: $i,SY1913: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1913 @ tc_HOL_Obool ) ) @ SY1912 ) @ SV415 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1913 ) @ SV177 ) @ SY1912 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1913 ) @ SV177 ) @ SV415 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6123]) ).
thf(6365,plain,
! [SV178: $i,SV416: $i] :
( ( ! [SY1914: $i,SY1915: $i,SY1916: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1916 @ tc_HOL_Obool ) ) @ SY1915 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1916 @ tc_HOL_Obool ) ) @ SV416 ) @ SV178 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1916 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1916 @ tc_HOL_Obool ) ) @ SY1915 ) @ SV416 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1916 @ tc_HOL_Obool ) ) @ SY1914 ) @ SV178 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6124]) ).
thf(6366,plain,
! [SV179: $i,SV417: $i] :
( ( ! [SY1917: $i,SY1918: $i,SY1919: $i,SY1920: $i] :
( ~ ( ( SY1920 != SY1919 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1918 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1918 @ SY1917 ) @ SY1920 ) @ SV417 ) ) @ SY1919 ) @ SV179 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1918 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1918 @ SY1917 ) @ SY1919 ) @ SV179 ) ) @ SY1920 ) @ SV417 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6125]) ).
thf(6367,plain,
! [SV180: $i,SV418: $i] :
( ( ! [SY1921: $i,SY1922: $i,SY1923: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1923 @ tc_HOL_Obool ) ) @ SY1922 ) @ SY1921 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV418 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ SY1923 @ SV418 @ SV180 ) @ SY1922 ) ) @ ( hAPP @ ( c_Set_Oimage @ SY1923 @ SV418 @ SV180 ) @ SY1921 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6126]) ).
thf(6368,plain,
! [SV181: $i,SV419: $i] :
( ( ! [SY1924: $i,SY1925: $i,SY1926: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1926 @ SY1925 @ SY1924 ) @ SV419 ) @ SV181 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1924 @ SV181 ) @ SV419 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1924 @ SV181 ) @ SV419 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1926 @ SY1925 @ SY1924 ) @ SV419 ) @ SV181 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6127]) ).
thf(6369,plain,
! [SV182: $i,SV420: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV420 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV182 ) )
| ( SV420 = SV182 ) )
| ~ ( ( SV420 != SV182 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV420 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV182 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6128]) ).
thf(6370,plain,
! [SV183: $i,SV421: $i] :
( ( ! [SY1927: $i,SY1928: $i,SY1929: $i,SY1930: $i,SY1931: $i,SY1932: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1932 @ SY1931 @ SY1930 @ SY1929 ) @ SY1928 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY1927 @ SY1931 @ SY1930 @ SV421 ) @ SV183 ) )
| ! [SY1933: $i] :
( ( hAPP @ SY1929 @ ( hAPP @ SY1928 @ SY1933 ) )
= ( hAPP @ SV421 @ ( hAPP @ SV183 @ SY1933 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6129]) ).
thf(6371,plain,
! [SV184: $i,SV422: $i] :
( ( ~ ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
| ! [SY1423: $i,SY1424: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1423 ) @ SY1424 ) )
| ( ( hAPP @ SV184 @ SY1423 )
= ( hAPP @ SV184 @ SY1424 ) ) )
| ~ ( ( ( hAPP @ SV184 @ SY1423 )
!= ( hAPP @ SV184 @ SY1424 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1423 ) @ SY1424 ) ) ) ) )
| ~ ( ~ ! [SY1425: $i,SY1426: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1425 ) @ SY1426 ) )
| ( ( hAPP @ SV184 @ SY1425 )
= ( hAPP @ SV184 @ SY1426 ) ) )
| ~ ( ( ( hAPP @ SV184 @ SY1425 )
!= ( hAPP @ SV184 @ SY1426 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1425 ) @ SY1426 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6130]) ).
thf(6372,plain,
! [SV185: $i,SV423: $i] :
( ( ! [SY1938: $i,SY1939: $i,SY1940: $i] :
( ( ( hAPP @ SY1940 @ SY1939 )
!= SY1938 )
| ( ( c_Fun_Ofun__upd @ SV423 @ SV185 @ SY1940 @ SY1939 @ SY1938 )
= SY1940 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6131]) ).
thf(6373,plain,
! [SV186: $i,SV424: $i] :
( ( ! [SY1941: $i,SY1942: $i,SY1943: $i,SY1944: $i,SY1945: $i,SY1946: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1946 @ SY1945 ) @ SY1944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1943 @ SY1944 ) @ SY1942 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY1941 @ SV424 @ SV186 @ SY1946 @ SY1943 ) @ SY1945 ) @ SY1942 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6132]) ).
thf(6374,plain,
! [SV187: $i,SV425: $i] :
( ( ! [SY1947: $i,SY1948: $i,SY1949: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1949 ) @ SY1948 ) @ SY1947 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1949 ) @ SV425 ) @ SV187 ) )
| ~ ( ( SY1948 != SV425 )
| ( SY1947 != SV187 ) ) )
| ~ ( ~ ~ ( ( SY1948 != SV425 )
| ( SY1947 != SV187 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1949 ) @ SY1948 ) @ SY1947 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1949 ) @ SV425 ) @ SV187 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6133]) ).
thf(6375,plain,
! [SV188: $i,SV426: $i] :
( ( ( SV426 != SV188 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV426 ) @ SV188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6134]) ).
thf(6376,plain,
! [SV189: $i,SV427: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV427 ) @ SV189 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV189 ) @ SV427 ) )
| ( SV427 = SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6135]) ).
thf(6377,plain,
! [SV190: $i,SV428: $i] :
( ( ! [SY1950: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1950 @ tc_HOL_Obool ) ) @ SV428 ) @ SV190 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1950 @ tc_HOL_Obool ) ) @ SV190 ) @ SV428 )
= SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6136]) ).
thf(6378,plain,
! [SV191: $i,SV429: $i] :
( ( ! [SY1951: $i,SY1952: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1952 @ tc_HOL_Obool ) ) @ SY1951 ) @ SV429 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1952 @ tc_HOL_Obool ) ) @ SV429 ) @ SV191 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1952 @ tc_HOL_Obool ) ) @ SY1951 ) @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6137]) ).
thf(6379,plain,
! [SV192: $i,SV430: $i] :
( ( ! [SY1953: $i,SY1954: $i,SY1955: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1955 @ tc_HOL_Obool ) ) @ SY1954 ) @ SY1953 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1955 @ tc_HOL_Obool ) ) @ SV430 ) @ SV192 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1955 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1955 @ tc_HOL_Obool ) ) @ SY1954 ) @ SV192 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1955 @ tc_HOL_Obool ) ) @ SY1953 ) @ SV430 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6138]) ).
thf(6380,plain,
! [SV193: $i,SV431: $i] :
( ( ! [SY1956: $i] :
( ( SY1956 != SV431 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV193 @ tc_HOL_Obool ) ) @ SY1956 ) @ SV431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6139]) ).
thf(6381,plain,
! [SV194: $i,SV432: $i] :
( ( ! [SY1957: $i] :
( SY1957
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV432 ) @ SV194 ) @ SY1957 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6140]) ).
thf(6382,plain,
! [SV195: $i,SV433: $i] :
( ( ~ ( class_Orderings_Obot @ SV433 )
| ( class_Orderings_Obot @ ( tc_fun @ SV195 @ SV433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6141]) ).
thf(6383,plain,
! [SV196: $i,SV434: $i] :
( ( ! [SY1958: $i,SY1959: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1959 @ tc_HOL_Obool ) ) @ SY1958 ) @ SV434 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1959 @ tc_HOL_Obool ) ) @ SV434 ) @ SV196 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1959 @ tc_HOL_Obool ) ) @ SY1958 ) @ SV196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6142]) ).
thf(6384,plain,
! [SV197: $i,SV435: $i] :
( ( ! [SY1960: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SY1960 @ SV435 ) @ SV197 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV435 @ SV197 ) @ SV197 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV435 @ SV197 ) @ SV197 ) )
| ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SY1960 @ SV435 ) @ SV197 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6143]) ).
thf(6385,plain,
! [SV198: $i,SV436: $i] :
( ( ! [SY1961: $i] :
( ~ ( class_Orderings_Oorder @ SY1961 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1961 ) @ SV436 ) @ SV198 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1961 ) @ SV198 ) @ SV436 ) )
| ( SV436 = SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6144]) ).
thf(6386,plain,
! [SV199: $i,SV437: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) @ SV199 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) ) )
| ( SV199
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV199
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) @ SV199 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6145]) ).
thf(6387,plain,
! [SV200: $i,SV438: $i] :
( ( ! [SY1962: $i,SY1963: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1963 @ tc_HOL_Obool ) ) @ SY1962 ) @ SV438 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1963 @ tc_HOL_Obool ) ) @ SV200 ) @ SV438 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1963 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1963 @ tc_HOL_Obool ) ) @ SY1962 ) @ SV200 ) ) @ SV438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6146]) ).
thf(6388,plain,
! [SV201: $i,SV439: $i] :
( ( ! [SY1964: $i,SY1965: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1965 @ SY1964 @ SV439 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1965 @ SV201 @ SY1964 )
| ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1965 @ SV201 @ SV439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6147]) ).
thf(6389,plain,
! [SV202: $i,SV440: $i] :
( ( ! [SY1966: $i] :
~ ( ~ ( ~ ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY1966 @ SX3 ) )
| ! [SY1968: $i,SY1969: $i] : ( hBOOL @ ( hAPP @ SY1966 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV202 ) @ SY1968 ) @ SY1969 ) ) ) )
| ~ ( ~ ! [SY1970: $i,SY1971: $i] : ( hBOOL @ ( hAPP @ SY1966 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV202 ) @ SY1970 ) @ SY1971 ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY1966 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6148]) ).
thf(6390,plain,
! [SV203: $i,SV441: $i] :
( ( ! [SY1973: $i] :
( ~ ( class_Orderings_Oorder @ SY1973 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1973 ) @ SV441 ) @ SV203 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1973 ) @ SV203 ) @ SV441 ) )
| ( SV203 = SV441 ) )
| ~ ( ( SV203 != SV441 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1973 ) @ SV203 ) @ SV441 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6149]) ).
thf(6391,plain,
! [SV204: $i,SV442: $i] :
( ( ! [SY1974: $i,SY1975: $i,SY1976: $i,SY1977: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1977 @ ( tc_fun @ SY1976 @ tc_HOL_Obool ) ) ) @ SY1975 ) @ SY1974 ) @ SV442 ) @ SV204 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1975 @ SV442 ) @ SV204 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1974 @ SV442 ) @ SV204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6150]) ).
thf(6392,plain,
! [SV205: $i,SV443: $i] :
( ( ! [SY1978: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SY1978 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SV443 ) @ SV205 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1978 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SY1978 @ tc_HOL_Obool ) @ SV443 ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SY1978 @ tc_HOL_Obool ) @ SV205 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6151]) ).
thf(6393,plain,
! [SV206: $i,SV444: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV444 )
| ( class_Orderings_Opreorder @ ( tc_fun @ SV206 @ SV444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6152]) ).
thf(6394,plain,
! [SV207: $i,SV445: $i] :
( ( ! [SY1979: $i] :
( ~ ( class_Orderings_Opreorder @ SY1979 )
| ( SV445 != SV207 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1979 ) @ SV445 ) @ SV207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6153]) ).
thf(6395,plain,
! [SV208: $i,SV446: $i] :
( ( ! [SY1980: $i,SY1981: $i,SY1982: $i,SY1983: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1983 @ SY1982 ) @ SY1981 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1980 @ ( tc_fun @ SV446 @ tc_HOL_Obool ) ) ) @ SY1983 ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV208 @ SY1982 ) @ SY1981 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6154]) ).
thf(6396,plain,
! [SV209: $i,SV447: $i] :
( ( ! [SY1984: $i,SY1985: $i,SY1986: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1986 @ SY1985 @ SY1984 )
| ( ( hAPP @ ( hAPP @ SY1984 @ SV447 ) @ ( hAPP @ ( hAPP @ SY1984 @ SV447 ) @ SV209 ) )
= ( hAPP @ ( hAPP @ SY1984 @ SV447 ) @ SV209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6155]) ).
thf(6397,plain,
! [SV210: $i,SV448: $i] :
( ( ! [SY1987: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1987 ) @ SV448 ) @ SV210 )
!= SV210 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6156]) ).
thf(6398,plain,
! [SV211: $i,SV449: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV449 )
| ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV211 @ SV449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6157]) ).
thf(6399,plain,
! [SV212: $i,SV450: $i] :
( ( ! [SY1988: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY1988 ) @ SV450 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1988 @ tc_HOL_Obool ) ) @ SV212 ) @ SV450 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY1988 ) @ SV212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6158]) ).
thf(6400,plain,
! [SV213: $i,SV451: $i] :
( ( ! [SY1989: $i,SY1990: $i] :
( ~ ( class_Orderings_Oorder @ SY1990 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1990 ) @ SY1989 ) @ SV451 ) )
| ( SY1989 != SV213 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1990 ) @ SV213 ) @ SV451 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6159]) ).
thf(6401,plain,
! [SV214: $i,SV452: $i] :
( ( ! [SY1991: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SY1991 ) @ SV452 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV452 ) @ SV214 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SY1991 ) @ SV214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6160]) ).
thf(6402,plain,
! [SV215: $i,SV453: $i] :
( ( ! [SY1992: $i,SY1993: $i] :
( ( SY1993 != SY1992 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SY1992 ) @ SV215 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SY1993 ) @ SV215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6161]) ).
thf(6403,plain,
! [SV216: $i,SV454: $i] :
( ( ! [SY1994: $i,SY1995: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1995 ) @ SY1994 ) @ SV454 ) @ SV216 ) )
| ( SY1994 = SV216 )
| ( hBOOL @ ( hAPP @ SV454 @ SV216 ) ) )
| ~ ( ~ ( ( SY1994 = SV216 )
| ( hBOOL @ ( hAPP @ SV454 @ SV216 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1995 ) @ SY1994 ) @ SV454 ) @ SV216 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6162]) ).
thf(6404,plain,
! [SV217: $i,SV455: $i] :
( ( ! [SY1996: $i,SY1997: $i,SY1998: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1998 ) @ SY1997 ) @ SY1996 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1998 ) @ SV455 ) @ SV217 ) )
| ~ ! [SY1999: $i] :
~ ( ~ ( ( SY1997
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1998 ) @ SV455 ) @ SY1999 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1998 ) @ SY1999 ) @ SY1996 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1998 ) @ SY1997 ) @ SY1999 )
!= SV455 )
| ( SY1996
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1998 ) @ SY1999 ) @ SV217 ) ) ) ) )
| ~ ( ~ ~ ! [SY2000: $i] :
~ ( ~ ( ( SY1997
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1998 ) @ SV455 ) @ SY2000 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1998 ) @ SY2000 ) @ SY1996 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1998 ) @ SY1997 ) @ SY2000 )
!= SV455 )
| ( SY1996
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1998 ) @ SY2000 ) @ SV217 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1998 ) @ SY1997 ) @ SY1996 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1998 ) @ SV455 ) @ SV217 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6163]) ).
thf(6405,plain,
! [SV218: $i,SV456: $i] :
( ( ~ ~ ( ~ ( class_Finite__Set_Ofinite @ SV456 )
| ~ ( class_Finite__Set_Ofinite @ SV218 ) )
| ( class_Finite__Set_Ofinite @ ( tc_fun @ SV456 @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6164]) ).
thf(6406,plain,
! [SV219: $i,SV457: $i] :
( ( ! [SY2001: $i,SY2002: $i,SY2003: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2003 @ SY2002 @ SY2001 ) @ SV457 ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2001 @ SV219 ) @ SV457 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6165]) ).
thf(6407,plain,
! [SV220: $i,SV458: $i] :
( ( ! [SY2004: $i] :
( ( SY2004 != SV458 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV220 @ tc_HOL_Obool ) ) @ SV458 ) @ SY2004 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6166]) ).
thf(6408,plain,
! [SV221: $i,SV459: $i] :
( ( ! [SY2005: $i,SY2006: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY2006 @ SY2005 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2005 @ SV459 ) @ SV221 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2005 @ SV221 ) @ SV459 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6167]) ).
thf(6409,plain,
! [SV222: $i,SV460: $i] :
( ( ~ ( class_Lattices_Oboolean__algebra @ SV460 )
| ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SV222 @ SV460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6168]) ).
thf(6410,plain,
! [SV223: $i,SV461: $i] :
( ( ! [SY2007: $i,SY2008: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY2008 @ SY2007 @ SV461 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY2008 ) @ tc_HOL_Obool ) ) @ SV223 ) @ SV461 ) )
| ( c_Hoare__Mirabelle_Ohoare__derivs @ SY2008 @ SY2007 @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6169]) ).
thf(6411,plain,
! [SV224: $i,SV462: $i] :
( ( ! [SY2009: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY2009 ) @ SV462 )
!= SV224 )
| ( SV462
= ( hAPP @ ( c_List_Orev @ SY2009 ) @ SV224 ) ) )
| ~ ( ( SV462
!= ( hAPP @ ( c_List_Orev @ SY2009 ) @ SV224 ) )
| ( ( hAPP @ ( c_List_Orev @ SY2009 ) @ SV462 )
= SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6170]) ).
thf(6412,plain,
! [SV225: $i,SV463: $i] :
( ( ! [SY2010: $i,SY2011: $i,SY2012: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY2012 @ SY2011 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2011 @ SY2010 ) @ SV463 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2011 @ SV463 ) @ SV225 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2011 @ SY2010 ) @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6171]) ).
thf(6413,plain,
! [SV226: $i,SV464: $i] :
( ( ! [SY2013: $i,SY2014: $i,SY2015: $i,SY2016: $i,SY2017: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY2017 @ SY2016 @ SY2015 @ SY2014 @ SY2013 ) @ SV464 ) @ SV226 ) )
| ~ ! [SY2018: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2014 @ SV464 ) @ SY2018 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2013 @ SY2018 ) @ SV226 ) ) ) )
| ~ ( ~ ~ ! [SY2019: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2014 @ SV464 ) @ SY2019 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2013 @ SY2019 ) @ SV226 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY2017 @ SY2016 @ SY2015 @ SY2014 @ SY2013 ) @ SV464 ) @ SV226 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6172]) ).
thf(6414,plain,
! [SV227: $i,SV465: $i] :
( ( ! [SY2020: $i,SY2021: $i,SY2022: $i,SY2023: $i,SY2024: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY2024 @ SY2023 @ SY2022 @ SY2021 @ SY2020 @ SV465 )
| ( ( hAPP @ ( hAPP @ SY2022 @ SV227 ) @ SV227 )
= SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6173]) ).
thf(6415,plain,
! [SV228: $i,SV466: $i] :
( ( ! [SY2025: $i,SY2026: $i,SY2027: $i,SY2028: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2028 @ SY2027 ) @ SY2026 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2025 @ ( tc_fun @ SV466 @ tc_HOL_Obool ) ) ) @ SY2028 ) @ SV228 ) @ SY2027 ) @ SY2026 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6174]) ).
thf(6416,plain,
! [SV229: $i,SV467: $i] :
( ( ! [SY2029: $i,SY2030: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2030 ) @ SY2029 ) @ SV467 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2030 @ tc_HOL_Obool ) ) @ SV467 ) @ SV229 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2030 ) @ SY2029 ) @ SV229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6175]) ).
thf(6417,plain,
! [SV230: $i,SV468: $i] :
( ( ! [SY2031: $i,SY2032: $i] :
( ~ ( class_Orderings_Oorder @ SY2032 )
| ( SY2031 != SV468 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2032 ) @ SV230 ) @ SV468 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2032 ) @ SV230 ) @ SY2031 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6176]) ).
thf(6418,plain,
! [SV231: $i,SV469: $i] :
( ( ! [SY2033: $i] :
( ~ ( class_Orderings_Oorder @ SY2033 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2033 ) @ SV469 ) @ SV231 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2033 ) @ SV231 ) @ SV469 ) )
| ( SV231 = SV469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6177]) ).
thf(6419,plain,
! [SV232: $i,SV470: $i] :
( ( ~ ( class_Orderings_Oorder @ SV470 )
| ( class_Orderings_Oorder @ ( tc_fun @ SV232 @ SV470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6178]) ).
thf(6420,plain,
! [SV233: $i,SV471: $i] :
( ( ! [SY2034: $i,SY2035: $i,SY2036: $i,SY2037: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2037 @ SY2036 ) @ SY2035 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2034 @ ( tc_fun @ SV471 @ tc_HOL_Obool ) ) ) @ SV233 ) @ SY2037 ) @ SY2036 ) @ SY2035 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6179]) ).
thf(6421,plain,
! [SV234: $i,SV472: $i] :
( ( ! [SY2038: $i,SY2039: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2039 @ tc_HOL_Obool ) ) @ SY2038 ) @ SV472 ) @ SV234 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SY2038 @ SV234 ) )
| ( hBOOL @ ( hAPP @ SV472 @ SV234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6180]) ).
thf(6422,plain,
! [SV235: $i,SV473: $i] :
( ( ! [SY2040: $i,SY2041: $i,SY2042: $i,SY2043: $i,SY2044: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2044 @ SY2043 @ SY2042 @ SY2041 @ SY2040 )
| ~ ( ~ ( ( ( hAPP @ SY2042 @ SV473 )
!= ( hAPP @ SY2042 @ SV235 ) )
| ( SV473 = SV235 ) )
| ~ ( ( SV473 != SV235 )
| ( ( hAPP @ SY2042 @ SV473 )
= ( hAPP @ SY2042 @ SV235 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6181]) ).
thf(6423,plain,
! [SV236: $i,SV474: $i] :
( ( ! [SY2045: $i,SY2046: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2046 @ tc_HOL_Obool ) ) @ SY2045 ) @ SV474 ) @ SV236 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY2045 @ SV236 ) )
| ~ ( hBOOL @ ( hAPP @ SV474 @ SV236 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6182]) ).
thf(6424,plain,
! [SV237: $i,SV475: $i] :
( ( ! [SY2047: $i] :
( ~ ( c_Predicate_Oreflp @ SY2047 @ SV475 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV475 @ SV237 ) @ SV237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6183]) ).
thf(6425,plain,
! [SV238: $i,SV476: $i] :
( ( ! [SY2048: $i,SY2049: $i,SY2050: $i,SY2051: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2051 @ SY2050 @ SY2049 @ SY2048 @ SV476 )
| ( ( hAPP @ SY2048 @ ( hAPP @ SY2049 @ SV238 ) )
= SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6184]) ).
thf(6426,plain,
! [SV239: $i,SV477: $i] :
( ( ~ ~ ! [SY2052: $i] :
~ ( hBOOL @ ( hAPP @ SV477 @ SY2052 ) )
| ( hBOOL @ ( hAPP @ SV477 @ ( c_Hilbert__Choice_OEps @ SV239 @ SV477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6185]) ).
thf(6427,plain,
! [SV240: $i,SV478: $i] :
( ( ! [SY2053: $i,SY2054: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2054 @ tc_HOL_Obool ) ) @ SY2053 ) @ SV478 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2054 @ tc_HOL_Obool ) ) @ SY2053 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2054 ) @ SV240 ) @ SV478 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6186]) ).
thf(6428,plain,
! [SV241: $i,SV479: $i] :
( ( ! [SY2055: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2055 @ tc_HOL_Obool ) ) @ SV479 ) @ SV241 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2055 @ tc_HOL_Obool ) ) @ SV241 ) @ SV479 ) )
| ( SV479 = SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6187]) ).
thf(6429,plain,
! [SV242: $i,SV480: $i] :
( ( ! [SY2056: $i] :
( ~ ( c_Wellfounded_OwfP @ SY2056 @ SV480 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2056 @ ( tc_fun @ SY2056 @ tc_HOL_Obool ) ) ) @ SV242 ) @ SV480 ) )
| ( c_Wellfounded_OwfP @ SY2056 @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6188]) ).
thf(6430,plain,
! [SV243: $i,SV481: $i] :
( ( ! [SY2057: $i] :
( ~ ( class_Orderings_Oorder @ SY2057 )
| ~ ( ~ ( ( SV481 != SV243 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2057 ) @ SV481 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2057 ) @ SV243 ) @ SV481 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2057 ) @ SV481 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2057 ) @ SV243 ) @ SV481 ) ) )
| ( SV481 = SV243 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6189]) ).
thf(6431,plain,
! [SV244: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SV244 )
= SV244 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6190]) ).
thf(6432,plain,
! [SV10: $i,SV254: $i,SV482: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV482 @ tc_HOL_Obool ) ) @ SV254 ) @ SV10 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV482 @ tc_HOL_Obool ) ) @ SV10 ) @ SV254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6200]) ).
thf(6433,plain,
! [SV11: $i,SV255: $i,SV483: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV483 @ tc_HOL_Obool ) ) @ SV255 ) @ SV11 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV483 @ tc_HOL_Obool ) ) @ SV11 ) @ SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6201]) ).
thf(6434,plain,
! [SV12: $i,SV256: $i,SV484: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV484 @ tc_HOL_Obool ) ) @ SV256 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV484 @ tc_HOL_Obool ) ) @ SV256 ) @ SV12 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV484 @ tc_HOL_Obool ) ) @ SV256 ) @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6202]) ).
thf(6435,plain,
! [SV13: $i,SV257: $i,SV485: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV485 @ tc_HOL_Obool ) ) @ SV257 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV485 @ tc_HOL_Obool ) ) @ SV257 ) @ SV13 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV485 @ tc_HOL_Obool ) ) @ SV257 ) @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6203]) ).
thf(6436,plain,
! [SV14: $i,SV258: $i,SV486: $i] :
( ( ! [SY2058: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2058 @ tc_HOL_Obool ) ) @ SV486 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2058 @ tc_HOL_Obool ) ) @ SV258 ) @ SV14 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2058 @ tc_HOL_Obool ) ) @ SV258 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2058 @ tc_HOL_Obool ) ) @ SV486 ) @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6204]) ).
thf(6437,plain,
! [SV15: $i,SV259: $i,SV487: $i] :
( ( ! [SY2059: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2059 @ tc_HOL_Obool ) ) @ SV487 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2059 @ tc_HOL_Obool ) ) @ SV259 ) @ SV15 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2059 @ tc_HOL_Obool ) ) @ SV259 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2059 @ tc_HOL_Obool ) ) @ SV487 ) @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6205]) ).
thf(6438,plain,
! [SV16: $i,SV260: $i,SV488: $i] :
( ( ! [SY2060: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2060 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2060 @ tc_HOL_Obool ) ) @ SV488 ) @ SV260 ) ) @ SV16 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2060 @ tc_HOL_Obool ) ) @ SV488 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2060 @ tc_HOL_Obool ) ) @ SV260 ) @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6206]) ).
thf(6439,plain,
! [SV17: $i,SV261: $i,SV489: $i] :
( ( ! [SY2061: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2061 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2061 @ tc_HOL_Obool ) ) @ SV489 ) @ SV261 ) ) @ SV17 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2061 @ tc_HOL_Obool ) ) @ SV489 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2061 @ tc_HOL_Obool ) ) @ SV261 ) @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6207]) ).
thf(6440,plain,
! [SV18: $i,SV262: $i,SV490: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV490 @ tc_HOL_Obool ) ) @ SV262 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV490 @ tc_HOL_Obool ) ) @ SV262 ) @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6208]) ).
thf(6441,plain,
! [SV19: $i,SV263: $i,SV491: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV491 @ tc_HOL_Obool ) ) @ SV263 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV491 @ tc_HOL_Obool ) ) @ SV19 ) @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6209]) ).
thf(6442,plain,
! [SV20: $i,SV264: $i,SV492: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV492 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV492 @ tc_HOL_Obool ) ) @ SV264 ) @ SV20 ) ) @ SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6210]) ).
thf(6443,plain,
! [SV21: $i,SV265: $i,SV493: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV493 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV493 @ tc_HOL_Obool ) ) @ SV265 ) @ SV21 ) ) @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6211]) ).
thf(6444,plain,
! [SV22: $i,SV266: $i,SV494: $i] :
( ( ! [SY2062: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2062 ) @ SV494 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2062 ) @ SV266 ) @ SV22 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2062 ) @ SV266 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2062 ) @ SV494 ) @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6212]) ).
thf(6445,plain,
! [SV23: $i,SV267: $i,SV495: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV495 ) @ SV267 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV495 ) @ SV267 ) @ SV23 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV495 ) @ SV267 ) @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6213]) ).
thf(6446,plain,
! [SV24: $i,SV268: $i,SV496: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV496 @ tc_HOL_Obool ) ) @ SV268 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV496 ) @ SV24 ) @ SV268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6214]) ).
thf(6447,plain,
! [SV25: $i,SV269: $i,SV497: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV497 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV497 @ tc_HOL_Obool ) ) @ SV269 ) @ SV25 ) ) @ SV25 )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV497 @ tc_HOL_Obool ) ) @ SV269 ) @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6215]) ).
thf(6448,plain,
! [SV26: $i,SV270: $i,SV498: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV498 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV498 @ tc_HOL_Obool ) ) @ SV270 ) @ SV26 ) ) @ SV270 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6216]) ).
thf(6449,plain,
! [SV27: $i,SV271: $i,SV499: $i] :
( ( ! [SY2063: $i] :
( ( c_Fun_Ofun__upd @ SY2063 @ SV499 @ SV271 @ SV27 @ ( hAPP @ SV271 @ SV27 ) )
= SV271 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6217]) ).
thf(6450,plain,
! [SV28: $i,SV272: $i,SV500: $i] :
( ( ! [SY2064: $i,SY2065: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SY2065 @ SY2064 @ SV500 @ SV272 @ SV28 ) @ SV272 )
= SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6218]) ).
thf(6451,plain,
! [SV30: $i,SV273: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV273 ) @ SV30 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV30 ) @ SV273 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6219]) ).
thf(6452,plain,
! [SV32: $i,SV274: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV274 ) @ SV32 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV32 ) @ SV274 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6220]) ).
thf(6453,plain,
! [SV33: $i,SV275: $i,SV501: $i] :
( ( ! [SY2066: $i,SY2067: $i,SY2068: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2068 @ SY2067 @ SY2066 @ SV501 ) @ SV275 ) @ SV33 )
= ( hAPP @ SV501 @ ( hAPP @ SV275 @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6221]) ).
thf(6454,plain,
! [SV34: $i,SV276: $i,SV502: $i] :
( ( ! [SY2069: $i,SY2070: $i,SY2071: $i,SY2072: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY2072 @ SY2071 @ SY2070 @ SY2069 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV502 @ SY2072 @ SY2070 @ SV276 ) @ SV34 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV502 @ SY2071 @ SY2070 @ ( hAPP @ ( c_Fun_Ocomp @ SY2072 @ SY2071 @ SV502 @ SY2069 ) @ SV276 ) ) @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6222]) ).
thf(6455,plain,
! [SV35: $i,SV277: $i,SV503: $i] :
( ( ! [SY2073: $i,SY2074: $i,SY2075: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2075 @ SY2074 @ SY2073 @ SV503 ) @ SV277 ) @ SV35 )
= ( hAPP @ SV503 @ ( hAPP @ SV277 @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6223]) ).
thf(6456,plain,
! [SV36: $i,SV278: $i,SV504: $i] :
( ( ! [SY2076: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2076 @ ( tc_fun @ SV504 @ tc_HOL_Obool ) ) ) @ SV278 ) @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6224]) ).
thf(6457,plain,
! [SV40: $i,SV282: $i,SV505: $i] :
( ( ! [SY2077: $i,SY2078: $i,SY2079: $i,SY2080: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2080 @ SY2079 @ SY2078 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2080 @ SY2077 @ SY2079 ) @ SV505 ) @ SV282 ) ) @ SV40 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2080 @ SY2077 @ SY2078 ) @ SV505 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2077 @ SY2079 @ SY2078 ) @ SV282 ) @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6228]) ).
thf(6458,plain,
! [SV41: $i,SV283: $i,SV506: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ SV506 @ SV283 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV283 @ SV506 ) @ SV41 ) )
= SV41 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6229]) ).
thf(6459,plain,
! [SV42: $i,SV284: $i,SV507: $i] :
( ( ! [SY2081: $i] :
( ( hAPP @ SY2081 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV507 @ SV507 ) @ SV284 ) @ SY2081 ) @ SV42 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV507 @ SV507 ) @ SV284 ) @ SY2081 ) @ ( hAPP @ SY2081 @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6230]) ).
thf(6460,plain,
! [SV43: $i,SV285: $i,SV508: $i] :
( ( ! [SY2082: $i,SY2083: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2083 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2083 @ SY2082 ) @ SV508 ) @ SV285 ) ) @ SV508 ) @ SV43 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2083 @ SY2082 ) @ SV508 ) @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6231]) ).
thf(6461,plain,
! [SV44: $i,SV286: $i,SV509: $i] :
( ( ! [SY2084: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2084 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2084 ) @ SV509 ) @ SV286 ) ) @ SV44 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2084 ) @ SV509 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2084 ) @ SV286 ) @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6232]) ).
thf(6462,plain,
! [SV48: $i,SV289: $i,SV510: $i] :
( ( ! [SY2085: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ SY2085 @ SV510 ) @ SV289 ) @ SV48 )
= SV289 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6235]) ).
thf(6463,plain,
! [SV49: $i,SV290: $i,SV511: $i] :
( ( ! [SY2086: $i,SY2087: $i,SY2088: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY2088 @ SY2087 @ SY2086 ) @ SV511 ) @ SV290 ) @ SV49 )
= ( hAPP @ SV511 @ ( hAPP @ SV290 @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6236]) ).
thf(6464,plain,
! [SV50: $i,SV291: $i,SV512: $i] :
( ( ! [SY2089: $i,SY2090: $i,SY2091: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY2091 @ SY2090 @ SY2089 ) @ SV512 ) @ SV291 ) @ SV50 )
= ( hAPP @ ( hAPP @ SV512 @ SV50 ) @ SV291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6237]) ).
thf(6465,plain,
! [SV51: $i,SV292: $i,SV513: $i] :
( ( ! [SY2092: $i,SY2093: $i,SY2094: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY2094 @ SY2093 @ SY2092 ) @ SV513 ) @ SV292 ) @ SV51 )
= ( hAPP @ ( hAPP @ SV513 @ SV51 ) @ ( hAPP @ SV292 @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6238]) ).
thf(6466,plain,
! [SV52: $i,SV293: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV293 ) @ SV52 ) ) )
= $true )
| ( ( SV293 = SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6239]) ).
thf(6467,plain,
! [SV53: $i] :
( ( ( hBOOL @ ( hAPP @ c_fNot @ SV53 ) )
= $false )
| ( ( ~ ( hBOOL @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6240]) ).
thf(6468,plain,
! [SV54: $i] :
( ( ( ~ ( hBOOL @ SV54 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_fNot @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6241]) ).
thf(6469,plain,
! [SV55: $i,SV294: $i] :
( ( ( ~ ( hBOOL @ SV294 )
| ~ ( hBOOL @ SV55 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV294 ) @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6242]) ).
thf(6470,plain,
! [SV56: $i,SV295: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV295 ) @ SV56 ) ) )
= $true )
| ( ( hBOOL @ SV295 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6243]) ).
thf(6471,plain,
! [SV57: $i,SV296: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV296 ) @ SV57 ) ) )
= $true )
| ( ( hBOOL @ SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6244]) ).
thf(6472,plain,
! [SV58: $i,SV297: $i] :
( ( ( ~ ( hBOOL @ SV297 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV297 ) @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6245]) ).
thf(6473,plain,
! [SV59: $i,SV298: $i] :
( ( ( ~ ( hBOOL @ SV298 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV59 ) @ SV298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6246]) ).
thf(6474,plain,
! [SV60: $i,SV299: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV299 ) @ SV60 ) )
| ( hBOOL @ SV299 ) )
= $true )
| ( ( hBOOL @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6247]) ).
thf(6475,plain,
! [SV61: $i,SV300: $i] :
( ( ( hBOOL @ SV300 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV300 ) @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6248]) ).
thf(6476,plain,
! [SV62: $i,SV301: $i] :
( ( ( ~ ( hBOOL @ SV301 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV62 ) @ SV301 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6249]) ).
thf(6477,plain,
! [SV63: $i,SV302: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV302 ) @ SV63 ) )
| ~ ( hBOOL @ SV302 ) )
= $true )
| ( ( hBOOL @ SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6250]) ).
thf(6478,plain,
! [SV64: $i,SV303: $i,SV514: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV514 @ tc_HOL_Obool ) ) @ SV303 ) @ SV64 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV514 @ tc_HOL_Obool ) ) @ SV64 ) @ SV303 )
= SV303 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6251]) ).
thf(6479,plain,
! [SV65: $i,SV304: $i,SV515: $i] :
( ( ! [SY2095: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2095 @ SV515 ) )
| ~ ( hBOOL @ ( hAPP @ SV304 @ SV515 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV65 @ tc_HOL_Obool ) ) @ SY2095 ) @ SV304 ) @ SV515 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6252]) ).
thf(6480,plain,
! [SV66: $i,SV305: $i,SV516: $i] :
( ( ! [SY2096: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2096 @ tc_HOL_Obool ) ) @ SV516 ) @ SV305 ) @ SV66 ) )
| ( hBOOL @ ( hAPP @ SV516 @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6253]) ).
thf(6481,plain,
! [SV67: $i,SV306: $i,SV517: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 )
= SV67 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 )
!= SV67 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6254]) ).
thf(6482,plain,
! [SV68: $i,SV307: $i,SV518: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV518 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV518 ) @ SV307 ) @ SV68 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV518 ) @ SV68 ) @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6255]) ).
thf(6483,plain,
! [SV69: $i,SV308: $i,SV519: $i] :
( ( ! [SY2097: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY2097 @ SV519 @ SV308 ) @ SV69 ) )
| ~ ! [SY1684: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ SY1684 ) @ SV69 ) ) )
| ~ ( ~ ~ ! [SY1685: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ SY1685 ) @ SV69 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY2097 @ SV519 @ SV308 ) @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6256]) ).
thf(6484,plain,
! [SV70: $i,SV309: $i] :
( ( ~ ( ~ ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
| ~ ( ~ ~ ! [SY1062: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1062 ) @ SY1062 ) )
| ~ ! [SY1063: $i,SY1064: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1064 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1064 ) @ SY1064 ) ) )
| ( ( hAPP @ SV70 @ SY1063 )
!= ( hAPP @ SV70 @ SY1064 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1064 ) @ SY1064 ) ) )
| ( ( hAPP @ SV70 @ SY1063 )
!= ( hAPP @ SV70 @ SY1064 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1064 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ! [SY1065: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1065 ) @ SY1065 ) )
| ~ ! [SY1066: $i,SY1067: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) ) ) ) )
| ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6257]) ).
thf(6485,plain,
! [SV71: $i,SV310: $i,SV520: $i] :
( ( ! [SY2100: $i] :
( ( SY2100 != SV520 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SY2100 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV520 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV520 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SY2100 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6258]) ).
thf(6486,plain,
! [SV72: $i,SV311: $i] :
( ( ( ~ ( class_Orderings_Otop @ SV311 ) )
= $true )
| ( ( class_Orderings_Otop @ ( tc_fun @ SV72 @ SV311 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6259]) ).
thf(6487,plain,
! [SV73: $i,SV312: $i,SV521: $i] :
( ( ! [SY2101: $i,SY2102: $i,SY2103: $i,SY2104: $i,SY2105: $i,SY2106: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2106 @ SY2105 @ SY2104 @ SY2103 ) @ SY2102 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY2101 @ SY2105 @ SY2104 @ SV521 ) @ SV312 ) )
| ( ( hAPP @ SY2103 @ ( hAPP @ SY2102 @ SV73 ) )
= ( hAPP @ SV521 @ ( hAPP @ SV312 @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6260]) ).
thf(6488,plain,
! [SV74: $i,SV313: $i,SV522: $i] :
( ( ! [SY2107: $i] :
( ~ ( class_Orderings_Oord @ SY2107 )
| ~ ! [SY2108: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2107 ) @ ( hAPP @ SV522 @ SY2108 ) ) @ ( hAPP @ SV313 @ SY2108 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV74 @ SY2107 ) ) @ SV522 ) @ SV313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6261]) ).
thf(6489,plain,
! [SV75: $i,SV314: $i,SV523: $i] :
( ( ! [SY2109: $i,SY2110: $i,SY2111: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2111 @ SY2110 ) @ SY2109 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV523 @ SY2110 ) @ SY2109 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV314 @ ( tc_fun @ SV75 @ tc_HOL_Obool ) ) ) @ SY2111 ) @ SV523 ) @ SY2110 ) @ SY2109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6262]) ).
thf(6490,plain,
! [SV77: $i,SV315: $i,SV524: $i] :
( ( ( SV524 != SV315 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV77 @ tc_HOL_Obool ) ) @ SV524 ) @ SV315 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV77 @ tc_HOL_Obool ) ) @ SV315 ) @ SV524 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6264]) ).
thf(6491,plain,
! [SV78: $i,SV316: $i,SV525: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) @ SV316 ) @ SV78 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV525 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ SV525 @ SV316 ) ) @ ( c_Predicate_OPowp @ SV525 @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6265]) ).
thf(6492,plain,
! [SV79: $i,SV317: $i] :
( ( ( SV317 != SV79 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV317 ) @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6266]) ).
thf(6493,plain,
! [SV80: $i,SV318: $i,SV526: $i] :
( ( ~ ( c_Equiv__Relations_Oequivp @ SV526 @ SV318 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV318 @ SV80 ) @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6267]) ).
thf(6494,plain,
! [SV81: $i,SV319: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV319 ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV81 @ SV319 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6268]) ).
thf(6495,plain,
! [SV82: $i,SV320: $i,SV527: $i] :
( ( ! [SY2112: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SY2112 @ SV527 @ SV320 )
| ( ( hAPP @ ( hAPP @ SV527 @ SV82 ) @ SV82 )
= SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6269]) ).
thf(6496,plain,
! [SV83: $i,SV321: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV321 )
!= ( hAPP @ c_Nat_OSuc @ SV83 ) )
= $true )
| ( ( SV321 = SV83 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6270]) ).
thf(6497,plain,
! [SV84: $i,SV322: $i,SV528: $i] :
( ( ! [SY2113: $i,SY2114: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2114 @ tc_HOL_Obool ) ) @ SY2113 ) @ SV528 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV322 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV322 @ SY2114 @ SV84 ) @ SY2113 ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV322 @ SY2114 @ SV84 ) @ SV528 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6271]) ).
thf(6498,plain,
! [SV85: $i,SV323: $i,SV529: $i] :
( ( ~ ~ ! [SY2115: $i] :
~ ( hBOOL @ ( hAPP @ SV529 @ SY2115 ) )
| ( SV323
!= ( c_Hilbert__Choice_OEps @ SV85 @ SV529 ) )
| ( hBOOL @ ( hAPP @ SV529 @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6272]) ).
thf(6499,plain,
! [SV86: $i,SV324: $i,SV530: $i] :
( ( ! [SY2116: $i] :
( ( SY2116 != SV530 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SY2116 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SY2116 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6273]) ).
thf(6500,plain,
! [SV87: $i,SV325: $i,SV531: $i] :
( ( ! [SY2117: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2117 @ tc_HOL_Obool ) ) @ SV531 ) @ SV325 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2117 @ tc_HOL_Obool ) ) @ SV325 ) @ SV87 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2117 @ tc_HOL_Obool ) ) @ SV531 ) @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6274]) ).
thf(6501,plain,
! [SV88: $i,SV326: $i,SV532: $i] :
( ( ! [SY2118: $i,SY2119: $i,SY2120: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2120 @ ( tc_fun @ SY2119 @ tc_HOL_Obool ) ) ) @ SY2118 ) @ SV532 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2118 @ SV326 ) @ SV88 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV532 @ SV326 ) @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6275]) ).
thf(6502,plain,
! [SV89: $i,SV327: $i] :
( ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV327 )
!= ( hAPP @ c_Int_ORep__Integ @ SV89 ) )
| ( SV327 = SV89 ) )
| ~ ( ( SV327 != SV89 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV327 )
= ( hAPP @ c_Int_ORep__Integ @ SV89 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6276]) ).
thf(6503,plain,
! [SV90: $i,SV328: $i,SV533: $i] :
( ( ! [SY2121: $i,SY2122: $i,SY2123: $i] :
( ~ ( ( SY2123 != SY2122 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY2121 @ SV533 @ SV328 @ SY2122 @ SV90 ) @ SY2123 )
= ( hAPP @ SV328 @ SY2123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6277]) ).
thf(6504,plain,
! [SV91: $i,SV329: $i,SV534: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV534 ) @ SV329 )
!= ( hAPP @ ( c_List_Orev @ SV534 ) @ SV91 ) )
| ( SV329 = SV91 ) )
| ~ ( ( SV329 != SV91 )
| ( ( hAPP @ ( c_List_Orev @ SV534 ) @ SV329 )
= ( hAPP @ ( c_List_Orev @ SV534 ) @ SV91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6278]) ).
thf(6505,plain,
! [SV92: $i,SV330: $i,SV535: $i] :
( ( ! [SY2124: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY2124 @ SV535 @ SV330 ) @ SV92 ) )
| ~ ! [SY1733: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ SY1733 ) ) )
| ~ ( ~ ~ ! [SY1734: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ SY1734 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY2124 @ SV535 @ SV330 ) @ SV92 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6279]) ).
thf(6506,plain,
! [SV93: $i,SV331: $i,SV536: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV536 ) @ tc_HOL_Obool ) ) @ SV331 ) @ SV93 ) )
| ( c_Hoare__Mirabelle_Ohoare__derivs @ SV536 @ SV93 @ SV331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6280]) ).
thf(6507,plain,
! [SV94: $i,SV332: $i] :
( ( ( ~ ( class_Groups_Ouminus @ SV332 ) )
= $true )
| ( ( class_Groups_Ouminus @ ( tc_fun @ SV94 @ SV332 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6281]) ).
thf(6508,plain,
! [SV95: $i,SV333: $i,SV537: $i] :
( ( ! [SY2127: $i,SY2128: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2128 @ tc_HOL_Obool ) ) @ SY2127 ) @ SV537 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2128 @ tc_HOL_Obool ) ) @ SV333 ) @ SV95 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2128 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2128 @ tc_HOL_Obool ) ) @ SY2127 ) @ SV333 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2128 @ tc_HOL_Obool ) ) @ SV537 ) @ SV95 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6282]) ).
thf(6509,plain,
! [SV96: $i,SV334: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV334 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV96 ) )
| ( SV334 = SV96 ) )
| ~ ( ( SV334 != SV96 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV334 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV96 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6283]) ).
thf(6510,plain,
! [SV97: $i,SV335: $i,SV538: $i] :
( ( ! [SY2129: $i,SY2130: $i,SY2131: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2131 @ ( tc_fun @ SY2130 @ tc_HOL_Obool ) ) ) @ SY2129 ) @ SV538 ) @ SV335 ) @ SV97 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2129 @ SV335 ) @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6284]) ).
thf(6511,plain,
! [SV98: $i,SV336: $i,SV539: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV539 @ tc_HOL_Obool ) ) @ SV336 ) @ SV98 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV539 @ tc_HOL_Obool ) ) @ SV336 ) @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6285]) ).
thf(6512,plain,
! [SV99: $i,SV337: $i,SV540: $i] :
( ( ! [SY2132: $i,SY2133: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY2133 @ SY2132 @ SV540 ) @ SV337 ) @ SV99 ) )
| ( hBOOL @ ( hAPP @ SV337 @ ( hAPP @ SV540 @ SV99 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV337 @ ( hAPP @ SV540 @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY2133 @ SY2132 @ SV540 ) @ SV337 ) @ SV99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6286]) ).
thf(6513,plain,
! [SV100: $i,SV338: $i,SV541: $i] :
( ( ! [SY2134: $i,SY2135: $i,SY2136: $i,SY2137: $i,SY2138: $i,SY2139: $i,SY2140: $i,SY2141: $i] :
( ( ( hAPP @ SY2141 @ ( hAPP @ SY2140 @ SY2139 ) )
!= ( hAPP @ SY2138 @ ( hAPP @ SY2137 @ SY2136 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2135 @ SY2134 @ SV541 @ SY2141 ) @ SY2140 ) @ SY2139 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV338 @ SY2134 @ SV100 @ SY2138 ) @ SY2137 ) @ SY2136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6287]) ).
thf(6514,plain,
! [SV101: $i,SV339: $i,SV542: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV339 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) @ SV339 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) @ SV339 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV339 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6288]) ).
thf(6515,plain,
! [SV102: $i,SV340: $i,SV543: $i] :
( ( ! [SY2142: $i,SY2143: $i,SY2144: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY2144 @ SY2143 @ SY2142 )
| ( ( hAPP @ ( hAPP @ SY2142 @ SV543 ) @ ( hAPP @ ( hAPP @ SY2142 @ SV340 ) @ SV102 ) )
= ( hAPP @ ( hAPP @ SY2142 @ SV340 ) @ ( hAPP @ ( hAPP @ SY2142 @ SV543 ) @ SV102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6289]) ).
thf(6516,plain,
! [SV103: $i,SV341: $i,SV544: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV103 ) )
| ! [SY2145: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SY2145 ) @ SV103 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SY2145 ) ) ) )
| ~ ( ~ ! [SY2146: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SY2146 ) @ SV103 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SY2146 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6290]) ).
thf(6517,plain,
! [SV104: $i,SV342: $i,SV545: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV545 @ tc_HOL_Obool ) ) @ SV342 ) @ SV104 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV545 @ tc_HOL_Obool ) ) @ SV342 ) @ SV104 )
= SV342 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6291]) ).
thf(6518,plain,
! [SV105: $i,SV343: $i,SV546: $i] :
( ( ! [SY2147: $i,SY2148: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SY2148 @ SY2147 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2147 @ SV546 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2147 @ SV343 ) @ SV105 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2147 @ SV546 ) @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6292]) ).
thf(6519,plain,
! [SV106: $i,SV344: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV344 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV344 ) @ SV106 ) @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6293]) ).
thf(6520,plain,
! [SV107: $i,SV345: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV345 ) )
= $true )
| ( ( class_Lattices_Olattice @ ( tc_fun @ SV107 @ SV345 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6294]) ).
thf(6521,plain,
! [SV108: $i,SV346: $i] :
( ( ( ~ ~ ! [SY1768: $i] :
~ ( hBOOL @ ( hAPP @ SV346 @ SY1768 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV346 @ ( c_Hilbert__Choice_OEps @ SV108 @ SV346 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6295]) ).
thf(6522,plain,
! [SV109: $i,SV347: $i,SV547: $i] :
( ( ! [SY2149: $i,SY2150: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2150 @ SY2149 ) @ SV547 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV347 @ SV109 @ SY2150 ) @ SV547 ) @ SY2149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6296]) ).
thf(6523,plain,
! [SV110: $i,SV348: $i,SV548: $i] :
( ( ! [SY2151: $i,SY2152: $i] :
~ ( ~ ( ( ( c_Fun_Ofun__upd @ SY2152 @ SY2151 @ SV548 @ SV348 @ SV110 )
!= SV548 )
| ( ( hAPP @ SV548 @ SV348 )
= SV110 ) )
| ~ ( ( ( hAPP @ SV548 @ SV348 )
!= SV110 )
| ( ( c_Fun_Ofun__upd @ SY2152 @ SY2151 @ SV548 @ SV348 @ SV110 )
= SV548 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6297]) ).
thf(6524,plain,
! [SV111: $i,SV349: $i,SV549: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV549 @ tc_HOL_Obool ) ) @ SV349 ) @ SV111 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV549 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ SV549 ) @ SV349 ) ) @ ( hAPP @ ( c_Set_OPow @ SV549 ) @ SV111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6298]) ).
thf(6525,plain,
! [SV112: $i,SV350: $i,SV550: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV112 ) )
| ! [SY2153: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV350 @ SY2153 ) @ SV112 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SY2153 ) ) ) )
| ~ ( ~ ! [SY2154: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV350 @ SY2154 ) @ SV112 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SY2154 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6299]) ).
thf(6526,plain,
! [SV113: $i,SV351: $i,SV551: $i] :
( ( ! [SY2155: $i] :
( ~ ( c_Predicate_Osymp @ SY2155 @ SV551 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV551 @ SV351 ) @ SV113 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV551 @ SV113 ) @ SV351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6300]) ).
thf(6527,plain,
! [SV114: $i,SV352: $i,SV552: $i] :
( ( ! [SY2156: $i,SY2157: $i,SY2158: $i] :
~ ( ~ ( ( SY2158 != SY2157 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY2156 @ SV552 @ SV352 @ SY2157 @ SV114 ) @ SY2158 )
= SV114 ) )
| ~ ( ~ ( ( SY2158 != SY2157 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY2156 @ SV552 @ SV352 @ SY2157 @ SV114 ) @ SY2158 )
= ( hAPP @ SV352 @ SY2158 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6301]) ).
thf(6528,plain,
! [SV115: $i,SV353: $i,SV553: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV553 @ tc_HOL_Obool ) ) @ SV353 ) @ SV115 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV553 ) @ SV115 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV553 ) @ SV353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6302]) ).
thf(6529,plain,
! [SV116: $i,SV354: $i] :
( ( ( ~ ~ ( ~ ( class_Enum_Oenum @ SV354 )
| ~ ( class_Enum_Oenum @ SV116 ) ) )
= $true )
| ( ( class_Enum_Oenum @ ( tc_fun @ SV354 @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6303]) ).
thf(6530,plain,
! [SV117: $i,SV355: $i,SV554: $i] :
( ( ! [SY2159: $i,SY2160: $i,SY2161: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2161 @ SY2160 ) @ SY2159 ) @ SV554 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2161 @ SY2160 ) @ SV355 ) @ SV117 ) )
| ~ ( ( SY2159 != SV355 )
| ( SV554 != SV117 ) ) )
| ~ ( ~ ~ ( ( SY2159 != SV355 )
| ( SV554 != SV117 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2161 @ SY2160 ) @ SY2159 ) @ SV554 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2161 @ SY2160 ) @ SV355 ) @ SV117 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6304]) ).
thf(6531,plain,
! [SV118: $i,SV356: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV356 ) @ SV118 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV118 ) @ SV356 ) )
| ( SV356 = SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6305]) ).
thf(6532,plain,
! [SV119: $i,SV357: $i,SV555: $i] :
( ( ! [SY2162: $i,SY2163: $i,SY2164: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2164 @ ( tc_fun @ SY2163 @ tc_HOL_Obool ) ) ) @ SY2162 ) @ SV555 ) @ SV357 ) @ SV119 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV555 @ SV357 ) @ SV119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6306]) ).
thf(6533,plain,
! [SV120: $i,SV358: $i,SV556: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
| ( SV358 = SV120 ) )
| ~ ( ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
| ( SV358 = SV120 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6307]) ).
thf(6534,plain,
! [SV121: $i,SV359: $i,SV557: $i] :
( ( ! [SY2165: $i] :
( ~ ( class_Orderings_Oord @ SY2165 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV557 @ SY2165 ) ) @ SV359 ) @ SV121 ) )
| ! [SY1797: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2165 ) @ ( hAPP @ SV359 @ SY1797 ) ) @ ( hAPP @ SV121 @ SY1797 ) ) ) )
| ~ ( ~ ! [SY1798: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2165 ) @ ( hAPP @ SV359 @ SY1798 ) ) @ ( hAPP @ SV121 @ SY1798 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV557 @ SY2165 ) ) @ SV359 ) @ SV121 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6308]) ).
thf(6535,plain,
! [SV122: $i,SV360: $i,SV558: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV558 @ SV360 ) )
| ( hBOOL @ ( hAPP @ SV558 @ ( c_Hilbert__Choice_OEps @ SV122 @ SV558 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6309]) ).
thf(6536,plain,
! [SV123: $i,SV361: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV361 @ ( c_Hilbert__Choice_OEps @ SV123 @ SV361 ) ) )
| ~ ! [SY1800: $i] :
~ ( hBOOL @ ( hAPP @ SV361 @ SY1800 ) ) )
| ~ ( ~ ~ ! [SY1801: $i] :
~ ( hBOOL @ ( hAPP @ SV361 @ SY1801 ) )
| ( hBOOL @ ( hAPP @ SV361 @ ( c_Hilbert__Choice_OEps @ SV123 @ SV361 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6310]) ).
thf(6537,plain,
! [SV124: $i,SV362: $i] :
( ( ( ~ ! [SY1802: $i] :
( ( hAPP @ SV362 @ SY1802 )
= ( hAPP @ SV124 @ SY1802 ) ) )
= $true )
| ( ( SV362 = SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6311]) ).
thf(6538,plain,
! [SV125: $i,SV363: $i,SV559: $i] :
( ( ! [SY2168: $i,SY2169: $i] :
( ~ ( c_Fun_Oinj__on @ SY2169 @ SY2168 @ SV559 @ SV363 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2169 @ tc_HOL_Obool ) ) @ SV125 ) @ SV363 ) )
| ( c_Fun_Oinj__on @ SY2169 @ SY2168 @ SV559 @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6312]) ).
thf(6539,plain,
! [SV126: $i,SV364: $i,SV560: $i] :
( ( ! [SY2170: $i] :
( ~ ( class_Orderings_Oord @ SY2170 )
| ( SV560 != SV364 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2170 ) @ SV364 ) @ SV126 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2170 ) @ SV560 ) @ SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6313]) ).
thf(6540,plain,
! [SV127: $i,SV365: $i,SV561: $i] :
( ( ! [SY2171: $i,SY2172: $i,SY2173: $i,SY2174: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2174 @ SY2173 @ SY2172 @ SY2171 ) @ SV561 )
!= SV365 )
| ( ( hAPP @ SY2171 @ ( hAPP @ SV561 @ SV127 ) )
= ( hAPP @ SV365 @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6314]) ).
thf(6541,plain,
! [SV128: $i,SV366: $i,SV562: $i] :
( ( ! [SY2175: $i,SY2176: $i,SY2177: $i] :
~ ( ~ ( ( SY2177 != SY2176 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY2175 @ SV562 @ SV366 @ SY2176 @ SV128 ) @ SY2177 )
= SV128 ) )
| ~ ( ~ ( ( SY2177 != SY2176 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY2175 @ SV562 @ SV366 @ SY2176 @ SV128 ) @ SY2177 )
= ( hAPP @ SV366 @ SY2177 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6315]) ).
thf(6542,plain,
! [SV129: $i,SV367: $i,SV563: $i] :
( ( ! [SY2178: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2178 ) @ SV563 ) @ SV367 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2178 ) @ SV563 ) @ SV129 ) )
| ( SV367 = SV129 ) )
| ~ ( ( SV367 != SV129 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2178 ) @ SV563 ) @ SV367 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2178 ) @ SV563 ) @ SV129 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6316]) ).
thf(6543,plain,
! [SV130: $i,SV368: $i,SV564: $i] :
( ( ! [SY2179: $i] :
( ~ ( class_Orderings_Opreorder @ SY2179 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2179 ) @ SV564 ) @ SV368 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2179 ) @ SV368 ) @ SV130 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2179 ) @ SV564 ) @ SV130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6317]) ).
thf(6544,plain,
! [SV131: $i,SV369: $i,SV565: $i] :
( ( ! [SY2180: $i] :
( ( SY2180 != SV565 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SY2180 ) @ SV131 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV565 ) @ SV131 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV565 ) @ SV131 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SY2180 ) @ SV131 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6318]) ).
thf(6545,plain,
! [SV132: $i,SV370: $i,SV566: $i] :
( ( ! [SY2181: $i,SY2182: $i,SY2183: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2183 ) @ SY2182 ) @ SY2181 )
!= SV566 )
| ( SV370
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2183 ) @ SY2181 ) @ SV132 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2183 ) @ SY2182 ) @ SV370 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2183 ) @ SV566 ) @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6319]) ).
thf(6546,plain,
! [SV133: $i,SV371: $i,SV567: $i] :
( ( ! [SY2184: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2184 ) @ SV567 ) @ SV371 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2184 ) @ SV133 ) @ SV371 ) )
| ( SV567 = SV133 ) )
| ~ ( ( SV567 != SV133 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2184 ) @ SV567 ) @ SV371 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2184 ) @ SV133 ) @ SV371 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6320]) ).
thf(6547,plain,
! [SV134: $i,SV372: $i,SV568: $i] :
( ( ! [SY2185: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2185 @ tc_HOL_Obool ) ) @ SV568 ) @ SV372 ) )
| ~ ( hBOOL @ ( hAPP @ SV568 @ SV134 ) )
| ( hBOOL @ ( hAPP @ SV372 @ SV134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6321]) ).
thf(6548,plain,
! [SV135: $i,SV373: $i,SV569: $i] :
( ( ! [SY2186: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SY2186 @ SV569 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV569 @ SV373 ) @ SV135 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV569 @ SV135 ) @ SV373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6322]) ).
thf(6549,plain,
! [SV136: $i,SV374: $i,SV570: $i] :
( ( ! [SY2187: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY2187 @ SV570 ) @ SV374 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY2187 @ SV570 ) @ SV136 ) )
| ( SV374 = SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6323]) ).
thf(6550,plain,
! [SV137: $i,SV375: $i,SV571: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV571 ) @ SV375 ) @ SV137 ) )
| ( hBOOL @ ( hAPP @ SV137 @ SV375 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV137 @ SV375 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV571 ) @ SV375 ) @ SV137 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6324]) ).
thf(6551,plain,
! [SV138: $i,SV376: $i,SV572: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV572 @ ( tc_fun @ SV572 @ tc_HOL_Obool ) ) ) @ SV376 ) @ SV138 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV572 @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ SV572 @ SV138 ) ) @ ( c_Wellfounded_Oaccp @ SV572 @ SV376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6325]) ).
thf(6552,plain,
! [SV139: $i,SV377: $i,SV573: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV573 @ tc_HOL_Obool ) ) @ SV377 ) @ SV139 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV573 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV573 @ tc_HOL_Obool ) ) @ SV139 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV573 @ tc_HOL_Obool ) ) @ SV377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6326]) ).
thf(6553,plain,
! [SV140: $i,SV378: $i,SV574: $i] :
( ( ! [SY2188: $i,SY2189: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2189 @ SY2188 ) @ SV574 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV378 @ SV140 @ SY2189 ) @ SV574 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6327]) ).
thf(6554,plain,
! [SV141: $i,SV379: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV379 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV141 ) )
| ( SV379 = SV141 ) )
| ~ ( ( SV379 != SV141 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV379 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV141 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6328]) ).
thf(6555,plain,
! [SV142: $i,SV380: $i,SV575: $i] :
( ( ! [SY2190: $i,SY2191: $i,SY2192: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2192 @ ( tc_fun @ SY2191 @ tc_HOL_Obool ) ) ) @ SY2190 ) @ SV575 ) @ SV380 ) @ SV142 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2190 @ SV380 ) @ SV142 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV575 @ SV380 ) @ SV142 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6329]) ).
thf(6556,plain,
! [SV143: $i,SV381: $i,SV576: $i] :
( ( ! [SY2193: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2193 @ tc_HOL_Obool ) ) @ SV576 ) @ SV381 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2193 @ tc_HOL_Obool ) ) @ SV576 ) @ SV143 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2193 @ tc_HOL_Obool ) ) @ SV576 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2193 @ tc_HOL_Obool ) ) @ SV381 ) @ SV143 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6330]) ).
thf(6557,plain,
! [SV144: $i,SV382: $i,SV577: $i] :
( ( ~ ( ~ ( ( SV577 != SV382 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV577 ) @ SV382 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV382 ) @ SV577 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV577 ) @ SV382 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV382 ) @ SV577 ) ) )
| ( SV577 = SV382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6331]) ).
thf(6558,plain,
! [SV145: $i,SV383: $i,SV578: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV578 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SV383 ) @ SV145 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV578 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SV578 @ tc_HOL_Obool ) @ SV145 ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SV578 @ tc_HOL_Obool ) @ SV383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6332]) ).
thf(6559,plain,
! [SV146: $i,SV384: $i,SV579: $i] :
( ( ! [SY2194: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2194 @ SV579 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV384 @ tc_HOL_Obool ) ) @ SY2194 ) @ SV146 ) )
| ( hBOOL @ ( hAPP @ SV146 @ SV579 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6333]) ).
thf(6560,plain,
! [SV147: $i,SV385: $i,SV580: $i] :
( ( ! [SY2195: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2195 @ tc_HOL_Obool ) ) @ SV580 ) @ SV385 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2195 @ tc_HOL_Obool ) ) @ SV385 ) @ SV147 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2195 @ tc_HOL_Obool ) ) @ SV580 ) @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6334]) ).
thf(6561,plain,
! [SV148: $i,SV386: $i,SV581: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV581 ) @ SV386 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV386 ) @ SV148 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV581 ) @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6335]) ).
thf(6562,plain,
! [SV149: $i,SV387: $i,SV582: $i] :
( ( ! [SY2196: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2196 @ SV582 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV387 @ tc_HOL_Obool ) ) @ SY2196 ) @ SV149 ) @ SV582 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6336]) ).
thf(6563,plain,
! [SV150: $i,SV388: $i,SV583: $i] :
( ( ! [SY2197: $i,SY2198: $i] :
( ~ ( class_Orderings_Oord @ SY2198 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2197 @ SY2198 ) ) @ SV583 ) @ SV388 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2198 ) @ ( hAPP @ SV583 @ SV150 ) ) @ ( hAPP @ SV388 @ SV150 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6337]) ).
thf(6564,plain,
! [SV151: $i,SV389: $i,SV584: $i] :
( ( ! [SY2199: $i,SY2200: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2200 @ SY2199 ) @ SV584 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV389 @ SV151 @ SY2200 ) @ SY2199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6338]) ).
thf(6565,plain,
! [SV152: $i,SV390: $i,SV585: $i] :
( ( ! [SY2201: $i,SY2202: $i,SY2203: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2203 @ SY2202 ) @ SY2201 ) @ SV585 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2203 @ SY2202 ) @ SV390 ) @ SV152 ) )
| ~ ( ( SY2201 != SV390 )
| ( SV585 != SV152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6339]) ).
thf(6566,plain,
! [SV153: $i,SV391: $i,SV586: $i] :
( ( ! [SY2204: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2204 @ tc_HOL_Obool ) ) @ SV586 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2204 ) @ SV153 ) @ SV586 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2204 ) @ SV153 ) @ SV391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6340]) ).
thf(6567,plain,
! [SV154: $i,SV392: $i,SV587: $i] :
( ( ! [SY2205: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2205 @ tc_HOL_Obool ) ) @ SV587 ) @ SV392 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2205 ) @ SV154 ) @ SV587 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2205 ) @ SV154 ) @ SV392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6341]) ).
thf(6568,plain,
! [SV155: $i,SV393: $i,SV588: $i] :
( ( ! [SY2206: $i,SY2207: $i,SY2208: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2208 @ SY2207 ) @ SY2206 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV588 @ SY2207 ) @ SY2206 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV393 @ ( tc_fun @ SV155 @ tc_HOL_Obool ) ) ) @ SV588 ) @ SY2208 ) @ SY2207 ) @ SY2206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6342]) ).
thf(6569,plain,
! [SV156: $i,SV394: $i,SV589: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
| ~ ( ( SV394 != SV156 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
| ~ ( ( SV394 != SV156 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6343]) ).
thf(6570,plain,
! [SV157: $i,SV395: $i,SV590: $i] :
( ( ! [SY2209: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2209 @ tc_HOL_Obool ) ) @ SV590 ) @ SV395 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2209 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2209 ) @ SV157 ) @ SV590 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2209 ) @ SV157 ) @ SV395 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6344]) ).
thf(6571,plain,
! [SV158: $i,SV396: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV396 ) )
= $true )
| ( ( class_Orderings_Oord @ ( tc_fun @ SV158 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6345]) ).
thf(6572,plain,
! [SV159: $i,SV397: $i,SV591: $i] :
( ( ! [SY2210: $i,SY2211: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2211 @ SY2210 @ SV591 ) @ SV397 ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV591 @ SV159 ) @ SV397 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV591 @ SV159 ) @ SV397 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2211 @ SY2210 @ SV591 ) @ SV397 ) @ SV159 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6346]) ).
thf(6573,plain,
! [SV160: $i,SV398: $i,SV592: $i] :
( ( ! [SY2212: $i,SY2213: $i] :
( ~ ( c_Predicate_Otransp @ SY2213 @ SY2212 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2212 @ SV592 ) @ SV398 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2212 @ SV398 ) @ SV160 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2212 @ SV592 ) @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6347]) ).
thf(6574,plain,
! [SV161: $i,SV399: $i,SV593: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV399 )
!= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV161 ) )
| ( SV399 = SV161 ) )
| ~ ( ( SV399 != SV161 )
| ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV399 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV161 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6348]) ).
thf(6575,plain,
! [SV162: $i,SV400: $i,SV594: $i] :
( ( ! [SY2214: $i,SY2215: $i] :
( ~ ( class_Orderings_Oord @ SY2215 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2214 @ SY2215 ) ) @ SV594 ) @ SV400 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2215 ) @ ( hAPP @ SV594 @ SV162 ) ) @ ( hAPP @ SV400 @ SV162 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6349]) ).
thf(6576,plain,
! [SV163: $i,SV401: $i,SV595: $i] :
( ( ! [SY2216: $i] :
( ~ ( class_Orderings_Oorder @ SY2216 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2216 ) @ SV595 ) @ SV401 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2216 ) @ SV163 ) @ SV595 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2216 ) @ SV163 ) @ SV401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6350]) ).
thf(6577,plain,
! [SV164: $i,SV402: $i] :
( ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV402 )
!= ( hAPP @ c_Nat_OSuc @ SV164 ) )
| ( SV402 = SV164 ) )
| ~ ( ( SV402 != SV164 )
| ( ( hAPP @ c_Nat_OSuc @ SV402 )
= ( hAPP @ c_Nat_OSuc @ SV164 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6351]) ).
thf(6578,plain,
! [SV165: $i,SV403: $i,SV596: $i] :
( ( ! [SY2217: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY2217 @ SV596 ) @ SV403 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV596 @ SV165 ) @ SV403 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY2217 @ SV596 ) @ SV165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6352]) ).
thf(6579,plain,
! [SV166: $i,SV404: $i,SV597: $i] :
( ( ! [SY2218: $i] :
( ~ ( class_Orderings_Oord @ SY2218 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2218 ) @ SV597 ) @ SV404 ) )
| ( SV404 != SV166 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2218 ) @ SV597 ) @ SV166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6353]) ).
thf(6580,plain,
! [SV167: $i,SV405: $i,SV598: $i] :
( ( ! [SY2219: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2219 @ tc_HOL_Obool ) ) @ SV598 ) @ SV405 ) @ SV167 ) )
| ( hBOOL @ ( hAPP @ SV405 @ SV167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6354]) ).
thf(6581,plain,
! [SV168: $i,SV406: $i,SV599: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV599 @ tc_HOL_Obool ) ) @ SV406 ) @ SV168 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV599 @ tc_HOL_Obool ) ) @ SV406 ) @ SV168 )
= SV168 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6355]) ).
thf(6582,plain,
! [SV169: $i,SV407: $i,SV600: $i] :
( ( ! [SY2220: $i,SY2221: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2221 @ tc_HOL_Obool ) ) @ SY2220 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SY2221 @ SV407 ) @ SV169 ) ) )
| ~ ! [SY2222: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SY2222 ) @ SV169 ) )
| ( SY2220
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SY2221 @ SV407 ) @ SY2222 ) ) ) )
| ~ ( ~ ~ ! [SY2223: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SY2223 ) @ SV169 ) )
| ( SY2220
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SY2221 @ SV407 ) @ SY2223 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2221 @ tc_HOL_Obool ) ) @ SY2220 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SY2221 @ SV407 ) @ SV169 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6356]) ).
thf(6583,plain,
! [SV170: $i,SV408: $i,SV601: $i] :
( ( ! [SY2224: $i,SY2225: $i,SY2226: $i] :
( ( SY2226 != SY2225 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY2224 @ SV601 @ SV408 ) @ SV170 ) @ SY2226 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY2224 @ SV601 @ SV408 ) @ SV170 ) @ SY2225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6357]) ).
thf(6584,plain,
! [SV171: $i,SV409: $i,SV602: $i] :
( ( ! [SY2227: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY2227 @ SV602 ) )
| ( hBOOL @ ( hAPP @ SV409 @ SV602 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV171 @ tc_HOL_Obool ) ) @ SV409 ) @ SY2227 ) @ SV602 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6358]) ).
thf(6585,plain,
! [SV172: $i,SV410: $i,SV603: $i] :
( ( ! [SY2228: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2228 @ tc_HOL_Obool ) ) @ SV603 ) @ SV410 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2228 @ tc_HOL_Obool ) ) @ SV410 ) @ SV172 ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2228 @ tc_HOL_Obool ) ) @ SV410 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2228 @ tc_HOL_Obool ) ) @ SV172 ) @ SV603 ) )
= SV603 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6359]) ).
thf(6586,plain,
! [SV173: $i,SV411: $i,SV604: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV604 )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV604 ) @ SV411 ) @ SV173 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV604 ) @ SV173 ) @ SV411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6360]) ).
thf(6587,plain,
! [SV174: $i,SV412: $i,SV605: $i] :
( ( ! [SY2229: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2229 @ SV605 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV412 @ tc_HOL_Obool ) ) @ SV174 ) @ SY2229 ) @ SV605 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6361]) ).
thf(6588,plain,
! [SV175: $i,SV413: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV413 ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV175 @ SV413 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6362]) ).
thf(6589,plain,
! [SV176: $i,SV414: $i] :
( ( ( ~ ( class_Groups_Ominus @ SV414 ) )
= $true )
| ( ( class_Groups_Ominus @ ( tc_fun @ SV176 @ SV414 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6363]) ).
thf(6590,plain,
! [SV177: $i,SV415: $i,SV606: $i] :
( ( ! [SY2230: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2230 @ tc_HOL_Obool ) ) @ SV606 ) @ SV415 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2230 ) @ SV177 ) @ SV606 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2230 ) @ SV177 ) @ SV415 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6364]) ).
thf(6591,plain,
! [SV178: $i,SV416: $i,SV607: $i] :
( ( ! [SY2231: $i,SY2232: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2232 @ tc_HOL_Obool ) ) @ SY2231 ) @ SV607 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2232 @ tc_HOL_Obool ) ) @ SV416 ) @ SV178 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2232 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2232 @ tc_HOL_Obool ) ) @ SY2231 ) @ SV416 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2232 @ tc_HOL_Obool ) ) @ SV607 ) @ SV178 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6365]) ).
thf(6592,plain,
! [SV179: $i,SV417: $i,SV608: $i] :
( ( ! [SY2233: $i,SY2234: $i,SY2235: $i] :
( ~ ( ( SY2235 != SY2234 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2233 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2233 @ SV608 ) @ SY2235 ) @ SV417 ) ) @ SY2234 ) @ SV179 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2233 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2233 @ SV608 ) @ SY2234 ) @ SV179 ) ) @ SY2235 ) @ SV417 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6366]) ).
thf(6593,plain,
! [SV180: $i,SV418: $i,SV609: $i] :
( ( ! [SY2236: $i,SY2237: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2237 @ tc_HOL_Obool ) ) @ SY2236 ) @ SV609 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV418 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ SY2237 @ SV418 @ SV180 ) @ SY2236 ) ) @ ( hAPP @ ( c_Set_Oimage @ SY2237 @ SV418 @ SV180 ) @ SV609 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6367]) ).
thf(6594,plain,
! [SV181: $i,SV419: $i,SV610: $i] :
( ( ! [SY2238: $i,SY2239: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2239 @ SY2238 @ SV610 ) @ SV419 ) @ SV181 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV610 @ SV181 ) @ SV419 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV610 @ SV181 ) @ SV419 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2239 @ SY2238 @ SV610 ) @ SV419 ) @ SV181 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6368]) ).
thf(6595,plain,
! [SV182: $i,SV420: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV420 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV182 ) )
| ( SV420 = SV182 ) )
| ~ ( ( SV420 != SV182 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV420 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV182 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6369]) ).
thf(6596,plain,
! [SV183: $i,SV421: $i,SV611: $i] :
( ( ! [SY2240: $i,SY2241: $i,SY2242: $i,SY2243: $i,SY2244: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2244 @ SY2243 @ SY2242 @ SY2241 ) @ SY2240 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV611 @ SY2243 @ SY2242 @ SV421 ) @ SV183 ) )
| ! [SY1933: $i] :
( ( hAPP @ SY2241 @ ( hAPP @ SY2240 @ SY1933 ) )
= ( hAPP @ SV421 @ ( hAPP @ SV183 @ SY1933 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6370]) ).
thf(6597,plain,
! [SV184: $i,SV422: $i] :
( ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
| ! [SY1423: $i,SY1424: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1423 ) @ SY1424 ) )
| ( ( hAPP @ SV184 @ SY1423 )
= ( hAPP @ SV184 @ SY1424 ) ) )
| ~ ( ( ( hAPP @ SV184 @ SY1423 )
!= ( hAPP @ SV184 @ SY1424 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1423 ) @ SY1424 ) ) ) ) )
| ~ ( ~ ! [SY1425: $i,SY1426: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1425 ) @ SY1426 ) )
| ( ( hAPP @ SV184 @ SY1425 )
= ( hAPP @ SV184 @ SY1426 ) ) )
| ~ ( ( ( hAPP @ SV184 @ SY1425 )
!= ( hAPP @ SV184 @ SY1426 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1425 ) @ SY1426 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6371]) ).
thf(6598,plain,
! [SV185: $i,SV423: $i,SV612: $i] :
( ( ! [SY2246: $i,SY2247: $i] :
( ( ( hAPP @ SY2247 @ SY2246 )
!= SV612 )
| ( ( c_Fun_Ofun__upd @ SV423 @ SV185 @ SY2247 @ SY2246 @ SV612 )
= SY2247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6372]) ).
thf(6599,plain,
! [SV186: $i,SV424: $i,SV613: $i] :
( ( ! [SY2248: $i,SY2249: $i,SY2250: $i,SY2251: $i,SY2252: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2252 @ SY2251 ) @ SY2250 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2249 @ SY2250 ) @ SY2248 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV613 @ SV424 @ SV186 @ SY2252 @ SY2249 ) @ SY2251 ) @ SY2248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6373]) ).
thf(6600,plain,
! [SV187: $i,SV425: $i,SV614: $i] :
( ( ! [SY2253: $i,SY2254: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2254 ) @ SY2253 ) @ SV614 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2254 ) @ SV425 ) @ SV187 ) )
| ~ ( ( SY2253 != SV425 )
| ( SV614 != SV187 ) ) )
| ~ ( ~ ~ ( ( SY2253 != SV425 )
| ( SV614 != SV187 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2254 ) @ SY2253 ) @ SV614 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2254 ) @ SV425 ) @ SV187 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6374]) ).
thf(6601,plain,
! [SV188: $i,SV426: $i] :
( ( ( SV426 != SV188 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV426 ) @ SV188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6375]) ).
thf(6602,plain,
! [SV189: $i,SV427: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV427 ) @ SV189 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV189 ) @ SV427 ) )
| ( SV427 = SV189 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6376]) ).
thf(6603,plain,
! [SV190: $i,SV428: $i,SV615: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV615 @ tc_HOL_Obool ) ) @ SV428 ) @ SV190 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV615 @ tc_HOL_Obool ) ) @ SV190 ) @ SV428 )
= SV190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6377]) ).
thf(6604,plain,
! [SV191: $i,SV429: $i,SV616: $i] :
( ( ! [SY2255: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2255 @ tc_HOL_Obool ) ) @ SV616 ) @ SV429 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2255 @ tc_HOL_Obool ) ) @ SV429 ) @ SV191 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2255 @ tc_HOL_Obool ) ) @ SV616 ) @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6378]) ).
thf(6605,plain,
! [SV192: $i,SV430: $i,SV617: $i] :
( ( ! [SY2256: $i,SY2257: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2257 @ tc_HOL_Obool ) ) @ SY2256 ) @ SV617 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2257 @ tc_HOL_Obool ) ) @ SV430 ) @ SV192 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2257 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2257 @ tc_HOL_Obool ) ) @ SY2256 ) @ SV192 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2257 @ tc_HOL_Obool ) ) @ SV617 ) @ SV430 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6379]) ).
thf(6606,plain,
! [SV193: $i,SV431: $i,SV618: $i] :
( ( ( SV618 != SV431 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV193 @ tc_HOL_Obool ) ) @ SV618 ) @ SV431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6380]) ).
thf(6607,plain,
! [SV194: $i,SV432: $i,SV619: $i] :
( ( SV619
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV432 ) @ SV194 ) @ SV619 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6381]) ).
thf(6608,plain,
! [SV195: $i,SV433: $i] :
( ( ( ~ ( class_Orderings_Obot @ SV433 ) )
= $true )
| ( ( class_Orderings_Obot @ ( tc_fun @ SV195 @ SV433 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6382]) ).
thf(6609,plain,
! [SV196: $i,SV434: $i,SV620: $i] :
( ( ! [SY2258: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2258 @ tc_HOL_Obool ) ) @ SV620 ) @ SV434 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2258 @ tc_HOL_Obool ) ) @ SV434 ) @ SV196 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2258 @ tc_HOL_Obool ) ) @ SV620 ) @ SV196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6383]) ).
thf(6610,plain,
! [SV197: $i,SV435: $i,SV621: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV621 @ SV435 ) @ SV197 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV435 @ SV197 ) @ SV197 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV435 @ SV197 ) @ SV197 ) )
| ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV621 @ SV435 ) @ SV197 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6384]) ).
thf(6611,plain,
! [SV198: $i,SV436: $i,SV622: $i] :
( ( ~ ( class_Orderings_Oorder @ SV622 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV622 ) @ SV436 ) @ SV198 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV622 ) @ SV198 ) @ SV436 ) )
| ( SV436 = SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6385]) ).
thf(6612,plain,
! [SV199: $i,SV437: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) @ SV199 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) ) )
| ( SV199
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV199
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) @ SV199 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6386]) ).
thf(6613,plain,
! [SV200: $i,SV438: $i,SV623: $i] :
( ( ! [SY2259: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2259 @ tc_HOL_Obool ) ) @ SV623 ) @ SV438 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2259 @ tc_HOL_Obool ) ) @ SV200 ) @ SV438 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2259 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2259 @ tc_HOL_Obool ) ) @ SV623 ) @ SV200 ) ) @ SV438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6387]) ).
thf(6614,plain,
! [SV201: $i,SV439: $i,SV624: $i] :
( ( ! [SY2260: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY2260 @ SV624 @ SV439 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY2260 @ SV201 @ SV624 )
| ( c_Hoare__Mirabelle_Ohoare__derivs @ SY2260 @ SV201 @ SV439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6388]) ).
thf(6615,plain,
! [SV202: $i,SV440: $i,SV625: $i] :
( ( ~ ( ~ ( ~ ! [SY2261: $i] : ( hBOOL @ ( hAPP @ SV625 @ SY2261 ) )
| ! [SY2262: $i,SY2263: $i] : ( hBOOL @ ( hAPP @ SV625 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV202 ) @ SY2262 ) @ SY2263 ) ) ) )
| ~ ( ~ ! [SY2264: $i,SY2265: $i] : ( hBOOL @ ( hAPP @ SV625 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV202 ) @ SY2264 ) @ SY2265 ) ) )
| ! [SY2266: $i] : ( hBOOL @ ( hAPP @ SV625 @ SY2266 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6389]) ).
thf(6616,plain,
! [SV203: $i,SV441: $i,SV626: $i] :
( ( ~ ( class_Orderings_Oorder @ SV626 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV441 ) @ SV203 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV203 ) @ SV441 ) )
| ( SV203 = SV441 ) )
| ~ ( ( SV203 != SV441 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV203 ) @ SV441 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6390]) ).
thf(6617,plain,
! [SV204: $i,SV442: $i,SV627: $i] :
( ( ! [SY2267: $i,SY2268: $i,SY2269: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2269 @ ( tc_fun @ SY2268 @ tc_HOL_Obool ) ) ) @ SY2267 ) @ SV627 ) @ SV442 ) @ SV204 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2267 @ SV442 ) @ SV204 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV627 @ SV442 ) @ SV204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6391]) ).
thf(6618,plain,
! [SV205: $i,SV443: $i,SV628: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV628 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SV443 ) @ SV205 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV628 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SV628 @ tc_HOL_Obool ) @ SV443 ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SV628 @ tc_HOL_Obool ) @ SV205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6392]) ).
thf(6619,plain,
! [SV206: $i,SV444: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV444 ) )
= $true )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV206 @ SV444 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6393]) ).
thf(6620,plain,
! [SV207: $i,SV445: $i,SV629: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV629 )
| ( SV445 != SV207 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV629 ) @ SV445 ) @ SV207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6394]) ).
thf(6621,plain,
! [SV208: $i,SV446: $i,SV630: $i] :
( ( ! [SY2270: $i,SY2271: $i,SY2272: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2272 @ SY2271 ) @ SY2270 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV630 @ ( tc_fun @ SV446 @ tc_HOL_Obool ) ) ) @ SY2272 ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV208 @ SY2271 ) @ SY2270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6395]) ).
thf(6622,plain,
! [SV209: $i,SV447: $i,SV631: $i] :
( ( ! [SY2273: $i,SY2274: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY2274 @ SY2273 @ SV631 )
| ( ( hAPP @ ( hAPP @ SV631 @ SV447 ) @ ( hAPP @ ( hAPP @ SV631 @ SV447 ) @ SV209 ) )
= ( hAPP @ ( hAPP @ SV631 @ SV447 ) @ SV209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6396]) ).
thf(6623,plain,
! [SV210: $i,SV448: $i,SV632: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV632 ) @ SV448 ) @ SV210 )
!= SV210 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6397]) ).
thf(6624,plain,
! [SV211: $i,SV449: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV449 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV211 @ SV449 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6398]) ).
thf(6625,plain,
! [SV212: $i,SV450: $i,SV633: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV633 ) @ SV450 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV633 @ tc_HOL_Obool ) ) @ SV212 ) @ SV450 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV633 ) @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6399]) ).
thf(6626,plain,
! [SV213: $i,SV451: $i,SV634: $i] :
( ( ! [SY2275: $i] :
( ~ ( class_Orderings_Oorder @ SY2275 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2275 ) @ SV634 ) @ SV451 ) )
| ( SV634 != SV213 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2275 ) @ SV213 ) @ SV451 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6400]) ).
thf(6627,plain,
! [SV214: $i,SV452: $i,SV635: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV635 ) @ SV452 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV452 ) @ SV214 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV635 ) @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6401]) ).
thf(6628,plain,
! [SV215: $i,SV453: $i,SV636: $i] :
( ( ! [SY2276: $i] :
( ( SY2276 != SV636 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV636 ) @ SV215 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SY2276 ) @ SV215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6402]) ).
thf(6629,plain,
! [SV216: $i,SV454: $i,SV637: $i] :
( ( ! [SY2277: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2277 ) @ SV637 ) @ SV454 ) @ SV216 ) )
| ( SV637 = SV216 )
| ( hBOOL @ ( hAPP @ SV454 @ SV216 ) ) )
| ~ ( ~ ( ( SV637 = SV216 )
| ( hBOOL @ ( hAPP @ SV454 @ SV216 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2277 ) @ SV637 ) @ SV454 ) @ SV216 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6403]) ).
thf(6630,plain,
! [SV217: $i,SV455: $i,SV638: $i] :
( ( ! [SY2278: $i,SY2279: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2279 ) @ SY2278 ) @ SV638 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2279 ) @ SV455 ) @ SV217 ) )
| ~ ! [SY2280: $i] :
~ ( ~ ( ( SY2278
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2279 ) @ SV455 ) @ SY2280 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2279 ) @ SY2280 ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2279 ) @ SY2278 ) @ SY2280 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2279 ) @ SY2280 ) @ SV217 ) ) ) ) )
| ~ ( ~ ~ ! [SY2281: $i] :
~ ( ~ ( ( SY2278
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2279 ) @ SV455 ) @ SY2281 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2279 ) @ SY2281 ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2279 ) @ SY2278 ) @ SY2281 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2279 ) @ SY2281 ) @ SV217 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2279 ) @ SY2278 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2279 ) @ SV455 ) @ SV217 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6404]) ).
thf(6631,plain,
! [SV218: $i,SV456: $i] :
( ( ( ~ ~ ( ~ ( class_Finite__Set_Ofinite @ SV456 )
| ~ ( class_Finite__Set_Ofinite @ SV218 ) ) )
= $true )
| ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV456 @ SV218 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6405]) ).
thf(6632,plain,
! [SV219: $i,SV457: $i,SV639: $i] :
( ( ! [SY2282: $i,SY2283: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2283 @ SY2282 @ SV639 ) @ SV457 ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV639 @ SV219 ) @ SV457 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6406]) ).
thf(6633,plain,
! [SV220: $i,SV458: $i,SV640: $i] :
( ( ( SV640 != SV458 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV220 @ tc_HOL_Obool ) ) @ SV458 ) @ SV640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6407]) ).
thf(6634,plain,
! [SV221: $i,SV459: $i,SV641: $i] :
( ( ! [SY2284: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY2284 @ SV641 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV641 @ SV459 ) @ SV221 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV641 @ SV221 ) @ SV459 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6408]) ).
thf(6635,plain,
! [SV222: $i,SV460: $i] :
( ( ( ~ ( class_Lattices_Oboolean__algebra @ SV460 ) )
= $true )
| ( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SV222 @ SV460 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6409]) ).
thf(6636,plain,
! [SV223: $i,SV461: $i,SV642: $i] :
( ( ! [SY2285: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY2285 @ SV642 @ SV461 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY2285 ) @ tc_HOL_Obool ) ) @ SV223 ) @ SV461 ) )
| ( c_Hoare__Mirabelle_Ohoare__derivs @ SY2285 @ SV642 @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6410]) ).
thf(6637,plain,
! [SV224: $i,SV462: $i,SV643: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV643 ) @ SV462 )
!= SV224 )
| ( SV462
= ( hAPP @ ( c_List_Orev @ SV643 ) @ SV224 ) ) )
| ~ ( ( SV462
!= ( hAPP @ ( c_List_Orev @ SV643 ) @ SV224 ) )
| ( ( hAPP @ ( c_List_Orev @ SV643 ) @ SV462 )
= SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6411]) ).
thf(6638,plain,
! [SV225: $i,SV463: $i,SV644: $i] :
( ( ! [SY2286: $i,SY2287: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY2287 @ SY2286 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2286 @ SV644 ) @ SV463 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2286 @ SV463 ) @ SV225 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2286 @ SV644 ) @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6412]) ).
thf(6639,plain,
! [SV226: $i,SV464: $i,SV645: $i] :
( ( ! [SY2288: $i,SY2289: $i,SY2290: $i,SY2291: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY2291 @ SY2290 @ SY2289 @ SY2288 @ SV645 ) @ SV464 ) @ SV226 ) )
| ~ ! [SY2292: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2288 @ SV464 ) @ SY2292 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2292 ) @ SV226 ) ) ) )
| ~ ( ~ ~ ! [SY2293: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2288 @ SV464 ) @ SY2293 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2293 ) @ SV226 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY2291 @ SY2290 @ SY2289 @ SY2288 @ SV645 ) @ SV464 ) @ SV226 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6413]) ).
thf(6640,plain,
! [SV227: $i,SV465: $i,SV646: $i] :
( ( ! [SY2294: $i,SY2295: $i,SY2296: $i,SY2297: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY2297 @ SY2296 @ SY2295 @ SY2294 @ SV646 @ SV465 )
| ( ( hAPP @ ( hAPP @ SY2295 @ SV227 ) @ SV227 )
= SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6414]) ).
thf(6641,plain,
! [SV228: $i,SV466: $i,SV647: $i] :
( ( ! [SY2298: $i,SY2299: $i,SY2300: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2300 @ SY2299 ) @ SY2298 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV647 @ ( tc_fun @ SV466 @ tc_HOL_Obool ) ) ) @ SY2300 ) @ SV228 ) @ SY2299 ) @ SY2298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6415]) ).
thf(6642,plain,
! [SV229: $i,SV467: $i,SV648: $i] :
( ( ! [SY2301: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2301 ) @ SV648 ) @ SV467 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2301 @ tc_HOL_Obool ) ) @ SV467 ) @ SV229 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2301 ) @ SV648 ) @ SV229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6416]) ).
thf(6643,plain,
! [SV230: $i,SV468: $i,SV649: $i] :
( ( ! [SY2302: $i] :
( ~ ( class_Orderings_Oorder @ SY2302 )
| ( SV649 != SV468 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2302 ) @ SV230 ) @ SV468 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2302 ) @ SV230 ) @ SV649 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6417]) ).
thf(6644,plain,
! [SV231: $i,SV469: $i,SV650: $i] :
( ( ~ ( class_Orderings_Oorder @ SV650 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV650 ) @ SV469 ) @ SV231 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV650 ) @ SV231 ) @ SV469 ) )
| ( SV231 = SV469 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6418]) ).
thf(6645,plain,
! [SV232: $i,SV470: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV470 ) )
= $true )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV232 @ SV470 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6419]) ).
thf(6646,plain,
! [SV233: $i,SV471: $i,SV651: $i] :
( ( ! [SY2303: $i,SY2304: $i,SY2305: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2305 @ SY2304 ) @ SY2303 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV651 @ ( tc_fun @ SV471 @ tc_HOL_Obool ) ) ) @ SV233 ) @ SY2305 ) @ SY2304 ) @ SY2303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6420]) ).
thf(6647,plain,
! [SV234: $i,SV472: $i,SV652: $i] :
( ( ! [SY2306: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2306 @ tc_HOL_Obool ) ) @ SV652 ) @ SV472 ) @ SV234 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV652 @ SV234 ) )
| ( hBOOL @ ( hAPP @ SV472 @ SV234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6421]) ).
thf(6648,plain,
! [SV235: $i,SV473: $i,SV653: $i] :
( ( ! [SY2307: $i,SY2308: $i,SY2309: $i,SY2310: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2310 @ SY2309 @ SY2308 @ SY2307 @ SV653 )
| ~ ( ~ ( ( ( hAPP @ SY2308 @ SV473 )
!= ( hAPP @ SY2308 @ SV235 ) )
| ( SV473 = SV235 ) )
| ~ ( ( SV473 != SV235 )
| ( ( hAPP @ SY2308 @ SV473 )
= ( hAPP @ SY2308 @ SV235 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6422]) ).
thf(6649,plain,
! [SV236: $i,SV474: $i,SV654: $i] :
( ( ! [SY2311: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2311 @ tc_HOL_Obool ) ) @ SV654 ) @ SV474 ) @ SV236 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV654 @ SV236 ) )
| ~ ( hBOOL @ ( hAPP @ SV474 @ SV236 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6423]) ).
thf(6650,plain,
! [SV237: $i,SV475: $i,SV655: $i] :
( ( ~ ( c_Predicate_Oreflp @ SV655 @ SV475 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV475 @ SV237 ) @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6424]) ).
thf(6651,plain,
! [SV238: $i,SV476: $i,SV656: $i] :
( ( ! [SY2312: $i,SY2313: $i,SY2314: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2314 @ SY2313 @ SY2312 @ SV656 @ SV476 )
| ( ( hAPP @ SV656 @ ( hAPP @ SY2312 @ SV238 ) )
= SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6425]) ).
thf(6652,plain,
! [SV239: $i,SV477: $i] :
( ( ( ~ ~ ! [SY2052: $i] :
~ ( hBOOL @ ( hAPP @ SV477 @ SY2052 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV477 @ ( c_Hilbert__Choice_OEps @ SV239 @ SV477 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6426]) ).
thf(6653,plain,
! [SV240: $i,SV478: $i,SV657: $i] :
( ( ! [SY2315: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2315 @ tc_HOL_Obool ) ) @ SV657 ) @ SV478 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2315 @ tc_HOL_Obool ) ) @ SV657 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2315 ) @ SV240 ) @ SV478 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6427]) ).
thf(6654,plain,
! [SV241: $i,SV479: $i,SV658: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV658 @ tc_HOL_Obool ) ) @ SV479 ) @ SV241 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV658 @ tc_HOL_Obool ) ) @ SV241 ) @ SV479 ) )
| ( SV479 = SV241 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6428]) ).
thf(6655,plain,
! [SV242: $i,SV480: $i,SV659: $i] :
( ( ~ ( c_Wellfounded_OwfP @ SV659 @ SV480 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV659 @ ( tc_fun @ SV659 @ tc_HOL_Obool ) ) ) @ SV242 ) @ SV480 ) )
| ( c_Wellfounded_OwfP @ SV659 @ SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6429]) ).
thf(6656,plain,
! [SV243: $i,SV481: $i,SV660: $i] :
( ( ~ ( class_Orderings_Oorder @ SV660 )
| ~ ( ~ ( ( SV481 != SV243 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) ) )
| ( SV481 = SV243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6430]) ).
thf(6657,plain,
! [SV14: $i,SV258: $i,SV486: $i,SV661: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV661 @ tc_HOL_Obool ) ) @ SV486 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV661 @ tc_HOL_Obool ) ) @ SV258 ) @ SV14 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV661 @ tc_HOL_Obool ) ) @ SV258 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV661 @ tc_HOL_Obool ) ) @ SV486 ) @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6436]) ).
thf(6658,plain,
! [SV15: $i,SV259: $i,SV487: $i,SV662: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV662 @ tc_HOL_Obool ) ) @ SV487 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV662 @ tc_HOL_Obool ) ) @ SV259 ) @ SV15 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV662 @ tc_HOL_Obool ) ) @ SV259 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV662 @ tc_HOL_Obool ) ) @ SV487 ) @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6437]) ).
thf(6659,plain,
! [SV16: $i,SV260: $i,SV488: $i,SV663: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV663 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV663 @ tc_HOL_Obool ) ) @ SV488 ) @ SV260 ) ) @ SV16 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV663 @ tc_HOL_Obool ) ) @ SV488 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV663 @ tc_HOL_Obool ) ) @ SV260 ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6438]) ).
thf(6660,plain,
! [SV17: $i,SV261: $i,SV489: $i,SV664: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV664 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV664 @ tc_HOL_Obool ) ) @ SV489 ) @ SV261 ) ) @ SV17 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV664 @ tc_HOL_Obool ) ) @ SV489 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV664 @ tc_HOL_Obool ) ) @ SV261 ) @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6439]) ).
thf(6661,plain,
! [SV22: $i,SV266: $i,SV494: $i,SV665: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV665 ) @ SV494 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV665 ) @ SV266 ) @ SV22 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV665 ) @ SV266 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV665 ) @ SV494 ) @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6444]) ).
thf(6662,plain,
! [SV27: $i,SV271: $i,SV499: $i,SV666: $i] :
( ( ( c_Fun_Ofun__upd @ SV666 @ SV499 @ SV271 @ SV27 @ ( hAPP @ SV271 @ SV27 ) )
= SV271 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6449]) ).
thf(6663,plain,
! [SV28: $i,SV272: $i,SV500: $i,SV667: $i] :
( ( ! [SY2316: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SY2316 @ SV667 @ SV500 @ SV272 @ SV28 ) @ SV272 )
= SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6450]) ).
thf(6664,plain,
! [SV33: $i,SV275: $i,SV501: $i,SV668: $i] :
( ( ! [SY2317: $i,SY2318: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2318 @ SY2317 @ SV668 @ SV501 ) @ SV275 ) @ SV33 )
= ( hAPP @ SV501 @ ( hAPP @ SV275 @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6453]) ).
thf(6665,plain,
! [SV34: $i,SV276: $i,SV502: $i,SV669: $i] :
( ( ! [SY2319: $i,SY2320: $i,SY2321: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY2321 @ SY2320 @ SY2319 @ SV669 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV502 @ SY2321 @ SY2319 @ SV276 ) @ SV34 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV502 @ SY2320 @ SY2319 @ ( hAPP @ ( c_Fun_Ocomp @ SY2321 @ SY2320 @ SV502 @ SV669 ) @ SV276 ) ) @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6454]) ).
thf(6666,plain,
! [SV35: $i,SV277: $i,SV503: $i,SV670: $i] :
( ( ! [SY2322: $i,SY2323: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2323 @ SY2322 @ SV670 @ SV503 ) @ SV277 ) @ SV35 )
= ( hAPP @ SV503 @ ( hAPP @ SV277 @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6455]) ).
thf(6667,plain,
! [SV36: $i,SV278: $i,SV504: $i,SV671: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV671 @ ( tc_fun @ SV504 @ tc_HOL_Obool ) ) ) @ SV278 ) @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6456]) ).
thf(6668,plain,
! [SV40: $i,SV282: $i,SV505: $i,SV672: $i] :
( ( ! [SY2324: $i,SY2325: $i,SY2326: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2326 @ SY2325 @ SY2324 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2326 @ SV672 @ SY2325 ) @ SV505 ) @ SV282 ) ) @ SV40 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2326 @ SV672 @ SY2324 ) @ SV505 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV672 @ SY2325 @ SY2324 ) @ SV282 ) @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6457]) ).
thf(6669,plain,
! [SV42: $i,SV284: $i,SV507: $i,SV673: $i] :
( ( ( hAPP @ SV673 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV507 @ SV507 ) @ SV284 ) @ SV673 ) @ SV42 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV507 @ SV507 ) @ SV284 ) @ SV673 ) @ ( hAPP @ SV673 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6459]) ).
thf(6670,plain,
! [SV43: $i,SV285: $i,SV508: $i,SV674: $i] :
( ( ! [SY2327: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2327 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2327 @ SV674 ) @ SV508 ) @ SV285 ) ) @ SV508 ) @ SV43 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2327 @ SV674 ) @ SV508 ) @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6460]) ).
thf(6671,plain,
! [SV44: $i,SV286: $i,SV509: $i,SV675: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV675 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV675 ) @ SV509 ) @ SV286 ) ) @ SV44 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV675 ) @ SV509 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV675 ) @ SV286 ) @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6461]) ).
thf(6672,plain,
! [SV48: $i,SV289: $i,SV510: $i,SV676: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBK @ SV676 @ SV510 ) @ SV289 ) @ SV48 )
= SV289 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6462]) ).
thf(6673,plain,
! [SV49: $i,SV290: $i,SV511: $i,SV677: $i] :
( ( ! [SY2328: $i,SY2329: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY2329 @ SY2328 @ SV677 ) @ SV511 ) @ SV290 ) @ SV49 )
= ( hAPP @ SV511 @ ( hAPP @ SV290 @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6463]) ).
thf(6674,plain,
! [SV50: $i,SV291: $i,SV512: $i,SV678: $i] :
( ( ! [SY2330: $i,SY2331: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY2331 @ SY2330 @ SV678 ) @ SV512 ) @ SV291 ) @ SV50 )
= ( hAPP @ ( hAPP @ SV512 @ SV50 ) @ SV291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6464]) ).
thf(6675,plain,
! [SV51: $i,SV292: $i,SV513: $i,SV679: $i] :
( ( ! [SY2332: $i,SY2333: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY2333 @ SY2332 @ SV679 ) @ SV513 ) @ SV292 ) @ SV51 )
= ( hAPP @ ( hAPP @ SV513 @ SV51 ) @ ( hAPP @ SV292 @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6465]) ).
thf(6676,plain,
! [SV52: $i,SV293: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV293 ) @ SV52 ) )
= $false )
| ( ( SV293 = SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6466]) ).
thf(6677,plain,
! [SV53: $i] :
( ( ( hBOOL @ SV53 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_fNot @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6467]) ).
thf(6678,plain,
! [SV54: $i] :
( ( ( hBOOL @ SV54 )
= $true )
| ( ( hBOOL @ ( hAPP @ c_fNot @ SV54 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6468]) ).
thf(6679,plain,
! [SV55: $i,SV294: $i] :
( ( ( ~ ( hBOOL @ SV294 ) )
= $true )
| ( ( ~ ( hBOOL @ SV55 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV294 ) @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6469]) ).
thf(6680,plain,
! [SV56: $i,SV295: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV295 ) @ SV56 ) )
= $false )
| ( ( hBOOL @ SV295 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6470]) ).
thf(6681,plain,
! [SV57: $i,SV296: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV296 ) @ SV57 ) )
= $false )
| ( ( hBOOL @ SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6471]) ).
thf(6682,plain,
! [SV58: $i,SV297: $i] :
( ( ( hBOOL @ SV297 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV297 ) @ SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6472]) ).
thf(6683,plain,
! [SV59: $i,SV298: $i] :
( ( ( hBOOL @ SV298 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV59 ) @ SV298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6473]) ).
thf(6684,plain,
! [SV60: $i,SV299: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV299 ) @ SV60 ) ) )
= $true )
| ( ( hBOOL @ SV299 )
= $true )
| ( ( hBOOL @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6474]) ).
thf(6685,plain,
! [SV62: $i,SV301: $i] :
( ( ( hBOOL @ SV301 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV62 ) @ SV301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6476]) ).
thf(6686,plain,
! [SV63: $i,SV302: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV302 ) @ SV63 ) ) )
= $true )
| ( ( ~ ( hBOOL @ SV302 ) )
= $true )
| ( ( hBOOL @ SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6477]) ).
thf(6687,plain,
! [SV64: $i,SV303: $i,SV514: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV514 @ tc_HOL_Obool ) ) @ SV303 ) @ SV64 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV514 @ tc_HOL_Obool ) ) @ SV64 ) @ SV303 )
= SV303 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6478]) ).
thf(6688,plain,
! [SV65: $i,SV304: $i,SV515: $i,SV680: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV680 @ SV515 ) )
| ~ ( hBOOL @ ( hAPP @ SV304 @ SV515 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV65 @ tc_HOL_Obool ) ) @ SV680 ) @ SV304 ) @ SV515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6479]) ).
thf(6689,plain,
! [SV66: $i,SV305: $i,SV516: $i,SV681: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV681 @ tc_HOL_Obool ) ) @ SV516 ) @ SV305 ) @ SV66 ) )
| ( hBOOL @ ( hAPP @ SV516 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6480]) ).
thf(6690,plain,
! [SV67: $i,SV306: $i,SV517: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 )
= SV67 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 )
!= SV67 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6481]) ).
thf(6691,plain,
! [SV68: $i,SV307: $i,SV518: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV518 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV518 ) @ SV307 ) @ SV68 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV518 ) @ SV68 ) @ SV307 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6482]) ).
thf(6692,plain,
! [SV69: $i,SV308: $i,SV519: $i,SV682: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV682 @ SV519 @ SV308 ) @ SV69 ) )
| ~ ! [SY1684: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ SY1684 ) @ SV69 ) ) )
| ~ ( ~ ~ ! [SY1685: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ SY1685 ) @ SV69 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV682 @ SV519 @ SV308 ) @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6483]) ).
thf(6693,plain,
! [SV70: $i,SV309: $i] :
( ( ~ ( ~ ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
| ~ ( ~ ~ ! [SY1062: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1062 ) @ SY1062 ) )
| ~ ! [SY1063: $i,SY1064: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1064 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1064 ) @ SY1064 ) ) )
| ( ( hAPP @ SV70 @ SY1063 )
!= ( hAPP @ SV70 @ SY1064 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1064 ) @ SY1064 ) ) )
| ( ( hAPP @ SV70 @ SY1063 )
!= ( hAPP @ SV70 @ SY1064 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1064 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6484]) ).
thf(6694,plain,
! [SV309: $i,SV70: $i] :
( ( ~ ( ~ ~ ( ~ ~ ! [SY1065: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1065 ) @ SY1065 ) )
| ~ ! [SY1066: $i,SY1067: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) ) ) ) )
| ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6484]) ).
thf(6695,plain,
! [SV71: $i,SV310: $i,SV520: $i,SV683: $i] :
( ( ( SV683 != SV520 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV683 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV520 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV520 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV683 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6485]) ).
thf(6696,plain,
! [SV72: $i,SV311: $i] :
( ( ( class_Orderings_Otop @ SV311 )
= $false )
| ( ( class_Orderings_Otop @ ( tc_fun @ SV72 @ SV311 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6486]) ).
thf(6697,plain,
! [SV73: $i,SV312: $i,SV521: $i,SV684: $i] :
( ( ! [SY2336: $i,SY2337: $i,SY2338: $i,SY2339: $i,SY2340: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2340 @ SY2339 @ SY2338 @ SY2337 ) @ SY2336 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV684 @ SY2339 @ SY2338 @ SV521 ) @ SV312 ) )
| ( ( hAPP @ SY2337 @ ( hAPP @ SY2336 @ SV73 ) )
= ( hAPP @ SV521 @ ( hAPP @ SV312 @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6487]) ).
thf(6698,plain,
! [SV74: $i,SV313: $i,SV522: $i,SV685: $i] :
( ( ~ ( class_Orderings_Oord @ SV685 )
| ~ ! [SY2341: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV685 ) @ ( hAPP @ SV522 @ SY2341 ) ) @ ( hAPP @ SV313 @ SY2341 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV74 @ SV685 ) ) @ SV522 ) @ SV313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6488]) ).
thf(6699,plain,
! [SV75: $i,SV314: $i,SV523: $i,SV686: $i] :
( ( ! [SY2342: $i,SY2343: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2343 @ SY2342 ) @ SV686 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV523 @ SY2342 ) @ SV686 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV314 @ ( tc_fun @ SV75 @ tc_HOL_Obool ) ) ) @ SY2343 ) @ SV523 ) @ SY2342 ) @ SV686 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6489]) ).
thf(6700,plain,
! [SV77: $i,SV315: $i,SV524: $i] :
( ( ( SV524 != SV315 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV77 @ tc_HOL_Obool ) ) @ SV524 ) @ SV315 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV77 @ tc_HOL_Obool ) ) @ SV315 ) @ SV524 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6490]) ).
thf(6701,plain,
! [SV78: $i,SV316: $i,SV525: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) @ SV316 ) @ SV78 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV525 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ SV525 @ SV316 ) ) @ ( c_Predicate_OPowp @ SV525 @ SV78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6491]) ).
thf(6702,plain,
! [SV79: $i,SV317: $i] :
( ( ( SV317 = SV79 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV317 ) @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6492]) ).
thf(6703,plain,
! [SV80: $i,SV318: $i,SV526: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequivp @ SV526 @ SV318 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV318 @ SV80 ) @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6493]) ).
thf(6704,plain,
! [SV81: $i,SV319: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV319 )
= $false )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV81 @ SV319 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6494]) ).
thf(6705,plain,
! [SV82: $i,SV320: $i,SV527: $i,SV687: $i] :
( ( ~ ( c_Finite__Set_Ofolding__one__idem @ SV687 @ SV527 @ SV320 )
| ( ( hAPP @ ( hAPP @ SV527 @ SV82 ) @ SV82 )
= SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6495]) ).
thf(6706,plain,
! [SV83: $i,SV321: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV321 )
= ( hAPP @ c_Nat_OSuc @ SV83 ) )
= $false )
| ( ( SV321 = SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6496]) ).
thf(6707,plain,
! [SV84: $i,SV322: $i,SV528: $i,SV688: $i] :
( ( ! [SY2344: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2344 @ tc_HOL_Obool ) ) @ SV688 ) @ SV528 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV322 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV322 @ SY2344 @ SV84 ) @ SV688 ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV322 @ SY2344 @ SV84 ) @ SV528 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6497]) ).
thf(6708,plain,
! [SV85: $i,SV323: $i,SV529: $i] :
( ( ( ~ ~ ! [SY2115: $i] :
~ ( hBOOL @ ( hAPP @ SV529 @ SY2115 ) ) )
= $true )
| ( ( ( SV323
!= ( c_Hilbert__Choice_OEps @ SV85 @ SV529 ) )
| ( hBOOL @ ( hAPP @ SV529 @ SV323 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6498]) ).
thf(6709,plain,
! [SV86: $i,SV324: $i,SV530: $i,SV689: $i] :
( ( ( SV689 != SV530 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6499]) ).
thf(6710,plain,
! [SV87: $i,SV325: $i,SV531: $i,SV690: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV690 @ tc_HOL_Obool ) ) @ SV531 ) @ SV325 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV690 @ tc_HOL_Obool ) ) @ SV325 ) @ SV87 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV690 @ tc_HOL_Obool ) ) @ SV531 ) @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6500]) ).
thf(6711,plain,
! [SV88: $i,SV326: $i,SV532: $i,SV691: $i] :
( ( ! [SY2345: $i,SY2346: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2346 @ ( tc_fun @ SY2345 @ tc_HOL_Obool ) ) ) @ SV691 ) @ SV532 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV691 @ SV326 ) @ SV88 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV532 @ SV326 ) @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6501]) ).
thf(6712,plain,
! [SV89: $i,SV327: $i] :
( ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV327 )
!= ( hAPP @ c_Int_ORep__Integ @ SV89 ) )
| ( SV327 = SV89 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6502]) ).
thf(6713,plain,
! [SV89: $i,SV327: $i] :
( ( ~ ( ( SV327 != SV89 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV327 )
= ( hAPP @ c_Int_ORep__Integ @ SV89 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6502]) ).
thf(6714,plain,
! [SV90: $i,SV328: $i,SV533: $i,SV692: $i] :
( ( ! [SY2347: $i,SY2348: $i] :
( ~ ( ( SY2348 != SY2347 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV692 @ SV533 @ SV328 @ SY2347 @ SV90 ) @ SY2348 )
= ( hAPP @ SV328 @ SY2348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6503]) ).
thf(6715,plain,
! [SV91: $i,SV329: $i,SV534: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV534 ) @ SV329 )
!= ( hAPP @ ( c_List_Orev @ SV534 ) @ SV91 ) )
| ( SV329 = SV91 ) )
| ~ ( ( SV329 != SV91 )
| ( ( hAPP @ ( c_List_Orev @ SV534 ) @ SV329 )
= ( hAPP @ ( c_List_Orev @ SV534 ) @ SV91 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6504]) ).
thf(6716,plain,
! [SV92: $i,SV330: $i,SV535: $i,SV693: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV693 @ SV535 @ SV330 ) @ SV92 ) )
| ~ ! [SY1733: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ SY1733 ) ) )
| ~ ( ~ ~ ! [SY1734: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ SY1734 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV693 @ SV535 @ SV330 ) @ SV92 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6505]) ).
thf(6717,plain,
! [SV93: $i,SV331: $i,SV536: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV536 ) @ tc_HOL_Obool ) ) @ SV331 ) @ SV93 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV536 @ SV93 @ SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6506]) ).
thf(6718,plain,
! [SV94: $i,SV332: $i] :
( ( ( class_Groups_Ouminus @ SV332 )
= $false )
| ( ( class_Groups_Ouminus @ ( tc_fun @ SV94 @ SV332 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6507]) ).
thf(6719,plain,
! [SV95: $i,SV333: $i,SV537: $i,SV694: $i] :
( ( ! [SY2351: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2351 @ tc_HOL_Obool ) ) @ SV694 ) @ SV537 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2351 @ tc_HOL_Obool ) ) @ SV333 ) @ SV95 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2351 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2351 @ tc_HOL_Obool ) ) @ SV694 ) @ SV333 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2351 @ tc_HOL_Obool ) ) @ SV537 ) @ SV95 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6508]) ).
thf(6720,plain,
! [SV96: $i,SV334: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV334 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV96 ) )
| ( SV334 = SV96 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6509]) ).
thf(6721,plain,
! [SV96: $i,SV334: $i] :
( ( ~ ( ( SV334 != SV96 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV334 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV96 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6509]) ).
thf(6722,plain,
! [SV97: $i,SV335: $i,SV538: $i,SV695: $i] :
( ( ! [SY2352: $i,SY2353: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2353 @ ( tc_fun @ SY2352 @ tc_HOL_Obool ) ) ) @ SV695 ) @ SV538 ) @ SV335 ) @ SV97 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV695 @ SV335 ) @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6510]) ).
thf(6723,plain,
! [SV98: $i,SV336: $i,SV539: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV539 @ tc_HOL_Obool ) ) @ SV336 ) @ SV98 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV539 @ tc_HOL_Obool ) ) @ SV336 ) @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6511]) ).
thf(6724,plain,
! [SV99: $i,SV337: $i,SV540: $i,SV696: $i] :
( ( ! [SY2354: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY2354 @ SV696 @ SV540 ) @ SV337 ) @ SV99 ) )
| ( hBOOL @ ( hAPP @ SV337 @ ( hAPP @ SV540 @ SV99 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV337 @ ( hAPP @ SV540 @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY2354 @ SV696 @ SV540 ) @ SV337 ) @ SV99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6512]) ).
thf(6725,plain,
! [SV100: $i,SV338: $i,SV541: $i,SV697: $i] :
( ( ! [SY2355: $i,SY2356: $i,SY2357: $i,SY2358: $i,SY2359: $i,SY2360: $i,SY2361: $i] :
( ( ( hAPP @ SY2361 @ ( hAPP @ SY2360 @ SY2359 ) )
!= ( hAPP @ SY2358 @ ( hAPP @ SY2357 @ SY2356 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2355 @ SV697 @ SV541 @ SY2361 ) @ SY2360 ) @ SY2359 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV338 @ SV697 @ SV100 @ SY2358 ) @ SY2357 ) @ SY2356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6513]) ).
thf(6726,plain,
! [SV101: $i,SV339: $i,SV542: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV339 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) @ SV339 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) @ SV339 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV339 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6514]) ).
thf(6727,plain,
! [SV102: $i,SV340: $i,SV543: $i,SV698: $i] :
( ( ! [SY2362: $i,SY2363: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY2363 @ SY2362 @ SV698 )
| ( ( hAPP @ ( hAPP @ SV698 @ SV543 ) @ ( hAPP @ ( hAPP @ SV698 @ SV340 ) @ SV102 ) )
= ( hAPP @ ( hAPP @ SV698 @ SV340 ) @ ( hAPP @ ( hAPP @ SV698 @ SV543 ) @ SV102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6515]) ).
thf(6728,plain,
! [SV103: $i,SV341: $i,SV544: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV103 ) )
| ! [SY2145: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SY2145 ) @ SV103 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SY2145 ) ) ) )
| ~ ( ~ ! [SY2146: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SY2146 ) @ SV103 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SY2146 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV103 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6516]) ).
thf(6729,plain,
! [SV104: $i,SV342: $i,SV545: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV545 @ tc_HOL_Obool ) ) @ SV342 ) @ SV104 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV545 @ tc_HOL_Obool ) ) @ SV342 ) @ SV104 )
= SV342 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6517]) ).
thf(6730,plain,
! [SV105: $i,SV343: $i,SV546: $i,SV699: $i] :
( ( ! [SY2364: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SY2364 @ SV699 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV546 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV343 ) @ SV105 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV546 ) @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6518]) ).
thf(6731,plain,
! [SV106: $i,SV344: $i] :
( ( ( class_Orderings_Opreorder @ SV344 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV344 ) @ SV106 ) @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6519]) ).
thf(6732,plain,
! [SV107: $i,SV345: $i] :
( ( ( class_Lattices_Olattice @ SV345 )
= $false )
| ( ( class_Lattices_Olattice @ ( tc_fun @ SV107 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6520]) ).
thf(6733,plain,
! [SV108: $i,SV346: $i] :
( ( ( ~ ! [SY1768: $i] :
~ ( hBOOL @ ( hAPP @ SV346 @ SY1768 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV346 @ ( c_Hilbert__Choice_OEps @ SV108 @ SV346 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6521]) ).
thf(6734,plain,
! [SV109: $i,SV347: $i,SV547: $i,SV700: $i] :
( ( ! [SY2365: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2365 @ SV700 ) @ SV547 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV347 @ SV109 @ SY2365 ) @ SV547 ) @ SV700 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6522]) ).
thf(6735,plain,
! [SV110: $i,SV348: $i,SV548: $i,SV701: $i] :
( ( ! [SY2366: $i] :
~ ( ~ ( ( ( c_Fun_Ofun__upd @ SY2366 @ SV701 @ SV548 @ SV348 @ SV110 )
!= SV548 )
| ( ( hAPP @ SV548 @ SV348 )
= SV110 ) )
| ~ ( ( ( hAPP @ SV548 @ SV348 )
!= SV110 )
| ( ( c_Fun_Ofun__upd @ SY2366 @ SV701 @ SV548 @ SV348 @ SV110 )
= SV548 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6523]) ).
thf(6736,plain,
! [SV111: $i,SV349: $i,SV549: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV549 @ tc_HOL_Obool ) ) @ SV349 ) @ SV111 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV549 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ SV549 ) @ SV349 ) ) @ ( hAPP @ ( c_Set_OPow @ SV549 ) @ SV111 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6524]) ).
thf(6737,plain,
! [SV112: $i,SV350: $i,SV550: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV112 ) )
| ! [SY2153: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV350 @ SY2153 ) @ SV112 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SY2153 ) ) ) )
| ~ ( ~ ! [SY2154: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV350 @ SY2154 ) @ SV112 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SY2154 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV112 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6525]) ).
thf(6738,plain,
! [SV113: $i,SV351: $i,SV551: $i,SV702: $i] :
( ( ~ ( c_Predicate_Osymp @ SV702 @ SV551 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV551 @ SV351 ) @ SV113 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV551 @ SV113 ) @ SV351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6526]) ).
thf(6739,plain,
! [SV114: $i,SV352: $i,SV552: $i,SV703: $i] :
( ( ! [SY2367: $i,SY2368: $i] :
~ ( ~ ( ( SY2368 != SY2367 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV703 @ SV552 @ SV352 @ SY2367 @ SV114 ) @ SY2368 )
= SV114 ) )
| ~ ( ~ ( ( SY2368 != SY2367 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV703 @ SV552 @ SV352 @ SY2367 @ SV114 ) @ SY2368 )
= ( hAPP @ SV352 @ SY2368 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6527]) ).
thf(6740,plain,
! [SV115: $i,SV353: $i,SV553: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV553 @ tc_HOL_Obool ) ) @ SV353 ) @ SV115 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV553 ) @ SV115 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV553 ) @ SV353 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6528]) ).
thf(6741,plain,
! [SV116: $i,SV354: $i] :
( ( ( ~ ( ~ ( class_Enum_Oenum @ SV354 )
| ~ ( class_Enum_Oenum @ SV116 ) ) )
= $false )
| ( ( class_Enum_Oenum @ ( tc_fun @ SV354 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6529]) ).
thf(6742,plain,
! [SV117: $i,SV355: $i,SV554: $i,SV704: $i] :
( ( ! [SY2369: $i,SY2370: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2370 @ SY2369 ) @ SV704 ) @ SV554 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2370 @ SY2369 ) @ SV355 ) @ SV117 ) )
| ~ ( ( SV704 != SV355 )
| ( SV554 != SV117 ) ) )
| ~ ( ~ ~ ( ( SV704 != SV355 )
| ( SV554 != SV117 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2370 @ SY2369 ) @ SV704 ) @ SV554 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2370 @ SY2369 ) @ SV355 ) @ SV117 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6530]) ).
thf(6743,plain,
! [SV118: $i,SV356: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV356 ) @ SV118 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV118 ) @ SV356 ) )
| ( SV356 = SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6531]) ).
thf(6744,plain,
! [SV119: $i,SV357: $i,SV555: $i,SV705: $i] :
( ( ! [SY2371: $i,SY2372: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2372 @ ( tc_fun @ SY2371 @ tc_HOL_Obool ) ) ) @ SV705 ) @ SV555 ) @ SV357 ) @ SV119 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV555 @ SV357 ) @ SV119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6532]) ).
thf(6745,plain,
! [SV120: $i,SV358: $i,SV556: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
| ( SV358 = SV120 ) )
| ~ ( ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
| ( SV358 = SV120 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6533]) ).
thf(6746,plain,
! [SV121: $i,SV359: $i,SV557: $i,SV706: $i] :
( ( ~ ( class_Orderings_Oord @ SV706 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV557 @ SV706 ) ) @ SV359 ) @ SV121 ) )
| ! [SY2373: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV706 ) @ ( hAPP @ SV359 @ SY2373 ) ) @ ( hAPP @ SV121 @ SY2373 ) ) ) )
| ~ ( ~ ! [SY2374: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV706 ) @ ( hAPP @ SV359 @ SY2374 ) ) @ ( hAPP @ SV121 @ SY2374 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV557 @ SV706 ) ) @ SV359 ) @ SV121 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6534]) ).
thf(6747,plain,
! [SV122: $i,SV360: $i,SV558: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV558 @ SV360 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV558 @ ( c_Hilbert__Choice_OEps @ SV122 @ SV558 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6535]) ).
thf(6748,plain,
! [SV123: $i,SV361: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV361 @ ( c_Hilbert__Choice_OEps @ SV123 @ SV361 ) ) )
| ~ ! [SY1800: $i] :
~ ( hBOOL @ ( hAPP @ SV361 @ SY1800 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6536]) ).
thf(6749,plain,
! [SV123: $i,SV361: $i] :
( ( ~ ( ~ ~ ! [SY1801: $i] :
~ ( hBOOL @ ( hAPP @ SV361 @ SY1801 ) )
| ( hBOOL @ ( hAPP @ SV361 @ ( c_Hilbert__Choice_OEps @ SV123 @ SV361 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6536]) ).
thf(6750,plain,
! [SV124: $i,SV362: $i] :
( ( ( ! [SY1802: $i] :
( ( hAPP @ SV362 @ SY1802 )
= ( hAPP @ SV124 @ SY1802 ) ) )
= $false )
| ( ( SV362 = SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6537]) ).
thf(6751,plain,
! [SV125: $i,SV363: $i,SV559: $i,SV707: $i] :
( ( ! [SY2375: $i] :
( ~ ( c_Fun_Oinj__on @ SY2375 @ SV707 @ SV559 @ SV363 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2375 @ tc_HOL_Obool ) ) @ SV125 ) @ SV363 ) )
| ( c_Fun_Oinj__on @ SY2375 @ SV707 @ SV559 @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6538]) ).
thf(6752,plain,
! [SV126: $i,SV364: $i,SV560: $i,SV708: $i] :
( ( ~ ( class_Orderings_Oord @ SV708 )
| ( SV560 != SV364 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV708 ) @ SV364 ) @ SV126 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV708 ) @ SV560 ) @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6539]) ).
thf(6753,plain,
! [SV127: $i,SV365: $i,SV561: $i,SV709: $i] :
( ( ! [SY2376: $i,SY2377: $i,SY2378: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2378 @ SY2377 @ SY2376 @ SV709 ) @ SV561 )
!= SV365 )
| ( ( hAPP @ SV709 @ ( hAPP @ SV561 @ SV127 ) )
= ( hAPP @ SV365 @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6540]) ).
thf(6754,plain,
! [SV128: $i,SV366: $i,SV562: $i,SV710: $i] :
( ( ! [SY2379: $i,SY2380: $i] :
~ ( ~ ( ( SY2380 != SY2379 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV710 @ SV562 @ SV366 @ SY2379 @ SV128 ) @ SY2380 )
= SV128 ) )
| ~ ( ~ ( ( SY2380 != SY2379 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV710 @ SV562 @ SV366 @ SY2379 @ SV128 ) @ SY2380 )
= ( hAPP @ SV366 @ SY2380 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6541]) ).
thf(6755,plain,
! [SV129: $i,SV367: $i,SV563: $i,SV711: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV367 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV129 ) )
| ( SV367 = SV129 ) )
| ~ ( ( SV367 != SV129 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV367 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV129 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6542]) ).
thf(6756,plain,
! [SV130: $i,SV368: $i,SV564: $i,SV712: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV712 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV712 ) @ SV564 ) @ SV368 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV712 ) @ SV368 ) @ SV130 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV712 ) @ SV564 ) @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6543]) ).
thf(6757,plain,
! [SV131: $i,SV369: $i,SV565: $i,SV713: $i] :
( ( ( SV713 != SV565 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV713 ) @ SV131 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV565 ) @ SV131 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV565 ) @ SV131 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV713 ) @ SV131 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6544]) ).
thf(6758,plain,
! [SV132: $i,SV370: $i,SV566: $i,SV714: $i] :
( ( ! [SY2381: $i,SY2382: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2382 ) @ SY2381 ) @ SV714 )
!= SV566 )
| ( SV370
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2382 ) @ SV714 ) @ SV132 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2382 ) @ SY2381 ) @ SV370 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2382 ) @ SV566 ) @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6545]) ).
thf(6759,plain,
! [SV133: $i,SV371: $i,SV567: $i,SV715: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV567 ) @ SV371 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV133 ) @ SV371 ) )
| ( SV567 = SV133 ) )
| ~ ( ( SV567 != SV133 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV567 ) @ SV371 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV133 ) @ SV371 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6546]) ).
thf(6760,plain,
! [SV134: $i,SV372: $i,SV568: $i,SV716: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV716 @ tc_HOL_Obool ) ) @ SV568 ) @ SV372 ) )
| ~ ( hBOOL @ ( hAPP @ SV568 @ SV134 ) )
| ( hBOOL @ ( hAPP @ SV372 @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6547]) ).
thf(6761,plain,
! [SV135: $i,SV373: $i,SV569: $i,SV717: $i] :
( ( ~ ( c_Equiv__Relations_Opart__equivp @ SV717 @ SV569 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV569 @ SV373 ) @ SV135 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV569 @ SV135 ) @ SV373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6548]) ).
thf(6762,plain,
! [SV136: $i,SV374: $i,SV570: $i,SV718: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV718 @ SV570 ) @ SV374 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV718 @ SV570 ) @ SV136 ) )
| ( SV374 = SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6549]) ).
thf(6763,plain,
! [SV137: $i,SV375: $i,SV571: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV571 ) @ SV375 ) @ SV137 ) )
| ( hBOOL @ ( hAPP @ SV137 @ SV375 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV137 @ SV375 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV571 ) @ SV375 ) @ SV137 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6550]) ).
thf(6764,plain,
! [SV138: $i,SV376: $i,SV572: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV572 @ ( tc_fun @ SV572 @ tc_HOL_Obool ) ) ) @ SV376 ) @ SV138 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV572 @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ SV572 @ SV138 ) ) @ ( c_Wellfounded_Oaccp @ SV572 @ SV376 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6551]) ).
thf(6765,plain,
! [SV139: $i,SV377: $i,SV573: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV573 @ tc_HOL_Obool ) ) @ SV377 ) @ SV139 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV573 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV573 @ tc_HOL_Obool ) ) @ SV139 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV573 @ tc_HOL_Obool ) ) @ SV377 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6552]) ).
thf(6766,plain,
! [SV140: $i,SV378: $i,SV574: $i,SV719: $i] :
( ( ! [SY2383: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2383 @ SV719 ) @ SV574 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV378 @ SV140 @ SY2383 ) @ SV574 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6553]) ).
thf(6767,plain,
! [SV141: $i,SV379: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV379 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV141 ) )
| ( SV379 = SV141 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6554]) ).
thf(6768,plain,
! [SV141: $i,SV379: $i] :
( ( ~ ( ( SV379 != SV141 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV379 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV141 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6554]) ).
thf(6769,plain,
! [SV142: $i,SV380: $i,SV575: $i,SV720: $i] :
( ( ! [SY2384: $i,SY2385: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2385 @ ( tc_fun @ SY2384 @ tc_HOL_Obool ) ) ) @ SV720 ) @ SV575 ) @ SV380 ) @ SV142 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV720 @ SV380 ) @ SV142 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV575 @ SV380 ) @ SV142 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6555]) ).
thf(6770,plain,
! [SV143: $i,SV381: $i,SV576: $i,SV721: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV576 ) @ SV381 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV576 ) @ SV143 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV576 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV381 ) @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6556]) ).
thf(6771,plain,
! [SV144: $i,SV382: $i,SV577: $i] :
( ( ~ ( ( SV577 != SV382 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV577 ) @ SV382 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV382 ) @ SV577 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV577 ) @ SV382 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV382 ) @ SV577 ) ) )
| ( SV577 = SV382 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6557]) ).
thf(6772,plain,
! [SV145: $i,SV383: $i,SV578: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV578 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SV383 ) @ SV145 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV578 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SV578 @ tc_HOL_Obool ) @ SV145 ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SV578 @ tc_HOL_Obool ) @ SV383 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6558]) ).
thf(6773,plain,
! [SV146: $i,SV384: $i,SV579: $i,SV722: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV722 @ SV579 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV384 @ tc_HOL_Obool ) ) @ SV722 ) @ SV146 ) )
| ( hBOOL @ ( hAPP @ SV146 @ SV579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6559]) ).
thf(6774,plain,
! [SV147: $i,SV385: $i,SV580: $i,SV723: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV723 @ tc_HOL_Obool ) ) @ SV580 ) @ SV385 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV723 @ tc_HOL_Obool ) ) @ SV385 ) @ SV147 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV723 @ tc_HOL_Obool ) ) @ SV580 ) @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6560]) ).
thf(6775,plain,
! [SV148: $i,SV386: $i,SV581: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV581 ) @ SV386 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV386 ) @ SV148 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV581 ) @ SV148 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6561]) ).
thf(6776,plain,
! [SV149: $i,SV387: $i,SV582: $i,SV724: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV724 @ SV582 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV387 @ tc_HOL_Obool ) ) @ SV724 ) @ SV149 ) @ SV582 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6562]) ).
thf(6777,plain,
! [SV150: $i,SV388: $i,SV583: $i,SV725: $i] :
( ( ! [SY2386: $i] :
( ~ ( class_Orderings_Oord @ SY2386 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV725 @ SY2386 ) ) @ SV583 ) @ SV388 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2386 ) @ ( hAPP @ SV583 @ SV150 ) ) @ ( hAPP @ SV388 @ SV150 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6563]) ).
thf(6778,plain,
! [SV151: $i,SV389: $i,SV584: $i,SV726: $i] :
( ( ! [SY2387: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2387 @ SV726 ) @ SV584 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV389 @ SV151 @ SY2387 ) @ SV726 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6564]) ).
thf(6779,plain,
! [SV152: $i,SV390: $i,SV585: $i,SV727: $i] :
( ( ! [SY2388: $i,SY2389: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2389 @ SY2388 ) @ SV727 ) @ SV585 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2389 @ SY2388 ) @ SV390 ) @ SV152 ) )
| ~ ( ( SV727 != SV390 )
| ( SV585 != SV152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6565]) ).
thf(6780,plain,
! [SV153: $i,SV391: $i,SV586: $i,SV728: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV728 @ tc_HOL_Obool ) ) @ SV586 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV728 ) @ SV153 ) @ SV586 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV728 ) @ SV153 ) @ SV391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6566]) ).
thf(6781,plain,
! [SV154: $i,SV392: $i,SV587: $i,SV729: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV729 @ tc_HOL_Obool ) ) @ SV587 ) @ SV392 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV729 ) @ SV154 ) @ SV587 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV729 ) @ SV154 ) @ SV392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6567]) ).
thf(6782,plain,
! [SV155: $i,SV393: $i,SV588: $i,SV730: $i] :
( ( ! [SY2390: $i,SY2391: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2391 @ SY2390 ) @ SV730 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV588 @ SY2390 ) @ SV730 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV393 @ ( tc_fun @ SV155 @ tc_HOL_Obool ) ) ) @ SV588 ) @ SY2391 ) @ SY2390 ) @ SV730 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6568]) ).
thf(6783,plain,
! [SV156: $i,SV394: $i,SV589: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
| ~ ( ( SV394 != SV156 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
| ~ ( ( SV394 != SV156 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6569]) ).
thf(6784,plain,
! [SV157: $i,SV395: $i,SV590: $i,SV731: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV731 @ tc_HOL_Obool ) ) @ SV590 ) @ SV395 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV731 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV731 ) @ SV157 ) @ SV590 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV731 ) @ SV157 ) @ SV395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6570]) ).
thf(6785,plain,
! [SV158: $i,SV396: $i] :
( ( ( class_Orderings_Oord @ SV396 )
= $false )
| ( ( class_Orderings_Oord @ ( tc_fun @ SV158 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6571]) ).
thf(6786,plain,
! [SV159: $i,SV397: $i,SV591: $i,SV732: $i] :
( ( ! [SY2392: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2392 @ SV732 @ SV591 ) @ SV397 ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV591 @ SV159 ) @ SV397 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV591 @ SV159 ) @ SV397 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2392 @ SV732 @ SV591 ) @ SV397 ) @ SV159 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6572]) ).
thf(6787,plain,
! [SV160: $i,SV398: $i,SV592: $i,SV733: $i] :
( ( ! [SY2393: $i] :
( ~ ( c_Predicate_Otransp @ SY2393 @ SV733 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV592 ) @ SV398 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV398 ) @ SV160 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV592 ) @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6573]) ).
thf(6788,plain,
! [SV161: $i,SV399: $i,SV593: $i] :
( ( ~ ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV399 )
!= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV161 ) )
| ( SV399 = SV161 ) )
| ~ ( ( SV399 != SV161 )
| ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV399 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV161 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6574]) ).
thf(6789,plain,
! [SV162: $i,SV400: $i,SV594: $i,SV734: $i] :
( ( ! [SY2394: $i] :
( ~ ( class_Orderings_Oord @ SY2394 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV734 @ SY2394 ) ) @ SV594 ) @ SV400 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2394 ) @ ( hAPP @ SV594 @ SV162 ) ) @ ( hAPP @ SV400 @ SV162 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6575]) ).
thf(6790,plain,
! [SV163: $i,SV401: $i,SV595: $i,SV735: $i] :
( ( ~ ( class_Orderings_Oorder @ SV735 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV735 ) @ SV595 ) @ SV401 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV735 ) @ SV163 ) @ SV595 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV735 ) @ SV163 ) @ SV401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6576]) ).
thf(6791,plain,
! [SV164: $i,SV402: $i] :
( ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV402 )
!= ( hAPP @ c_Nat_OSuc @ SV164 ) )
| ( SV402 = SV164 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6577]) ).
thf(6792,plain,
! [SV164: $i,SV402: $i] :
( ( ~ ( ( SV402 != SV164 )
| ( ( hAPP @ c_Nat_OSuc @ SV402 )
= ( hAPP @ c_Nat_OSuc @ SV164 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6577]) ).
thf(6793,plain,
! [SV165: $i,SV403: $i,SV596: $i,SV736: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV736 @ SV596 ) @ SV403 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV596 @ SV165 ) @ SV403 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV736 @ SV596 ) @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6578]) ).
thf(6794,plain,
! [SV166: $i,SV404: $i,SV597: $i,SV737: $i] :
( ( ~ ( class_Orderings_Oord @ SV737 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV737 ) @ SV597 ) @ SV404 ) )
| ( SV404 != SV166 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV737 ) @ SV597 ) @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6579]) ).
thf(6795,plain,
! [SV167: $i,SV405: $i,SV598: $i,SV738: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV738 @ tc_HOL_Obool ) ) @ SV598 ) @ SV405 ) @ SV167 ) )
| ( hBOOL @ ( hAPP @ SV405 @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6580]) ).
thf(6796,plain,
! [SV168: $i,SV406: $i,SV599: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV599 @ tc_HOL_Obool ) ) @ SV406 ) @ SV168 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV599 @ tc_HOL_Obool ) ) @ SV406 ) @ SV168 )
= SV168 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6581]) ).
thf(6797,plain,
! [SV169: $i,SV407: $i,SV600: $i,SV739: $i] :
( ( ! [SY2395: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2395 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SY2395 @ SV407 ) @ SV169 ) ) )
| ~ ! [SY2396: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SY2396 ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SY2395 @ SV407 ) @ SY2396 ) ) ) )
| ~ ( ~ ~ ! [SY2397: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SY2397 ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SY2395 @ SV407 ) @ SY2397 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2395 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SY2395 @ SV407 ) @ SV169 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6582]) ).
thf(6798,plain,
! [SV170: $i,SV408: $i,SV601: $i,SV740: $i] :
( ( ! [SY2398: $i,SY2399: $i] :
( ( SY2399 != SY2398 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV740 @ SV601 @ SV408 ) @ SV170 ) @ SY2399 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV740 @ SV601 @ SV408 ) @ SV170 ) @ SY2398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6583]) ).
thf(6799,plain,
! [SV171: $i,SV409: $i,SV602: $i,SV741: $i] :
( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV741 @ SV602 ) )
| ( hBOOL @ ( hAPP @ SV409 @ SV602 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV171 @ tc_HOL_Obool ) ) @ SV409 ) @ SV741 ) @ SV602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6584]) ).
thf(6800,plain,
! [SV172: $i,SV410: $i,SV603: $i,SV742: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV742 @ tc_HOL_Obool ) ) @ SV603 ) @ SV410 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV742 @ tc_HOL_Obool ) ) @ SV410 ) @ SV172 ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV742 @ tc_HOL_Obool ) ) @ SV410 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV742 @ tc_HOL_Obool ) ) @ SV172 ) @ SV603 ) )
= SV603 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6585]) ).
thf(6801,plain,
! [SV173: $i,SV411: $i,SV604: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV604 ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV604 ) @ SV411 ) @ SV173 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV604 ) @ SV173 ) @ SV411 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6586]) ).
thf(6802,plain,
! [SV174: $i,SV412: $i,SV605: $i,SV743: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV743 @ SV605 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV412 @ tc_HOL_Obool ) ) @ SV174 ) @ SV743 ) @ SV605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6587]) ).
thf(6803,plain,
! [SV175: $i,SV413: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV413 )
= $false )
| ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV175 @ SV413 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6588]) ).
thf(6804,plain,
! [SV176: $i,SV414: $i] :
( ( ( class_Groups_Ominus @ SV414 )
= $false )
| ( ( class_Groups_Ominus @ ( tc_fun @ SV176 @ SV414 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6589]) ).
thf(6805,plain,
! [SV177: $i,SV415: $i,SV606: $i,SV744: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV744 @ tc_HOL_Obool ) ) @ SV606 ) @ SV415 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV744 ) @ SV177 ) @ SV606 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV744 ) @ SV177 ) @ SV415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6590]) ).
thf(6806,plain,
! [SV178: $i,SV416: $i,SV607: $i,SV745: $i] :
( ( ! [SY2400: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2400 @ tc_HOL_Obool ) ) @ SV745 ) @ SV607 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2400 @ tc_HOL_Obool ) ) @ SV416 ) @ SV178 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2400 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2400 @ tc_HOL_Obool ) ) @ SV745 ) @ SV416 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2400 @ tc_HOL_Obool ) ) @ SV607 ) @ SV178 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6591]) ).
thf(6807,plain,
! [SV179: $i,SV417: $i,SV608: $i,SV746: $i] :
( ( ! [SY2401: $i,SY2402: $i] :
( ~ ( ( SY2402 != SY2401 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ SV608 ) @ SY2402 ) @ SV417 ) ) @ SY2401 ) @ SV179 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ SV608 ) @ SY2401 ) @ SV179 ) ) @ SY2402 ) @ SV417 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6592]) ).
thf(6808,plain,
! [SV180: $i,SV418: $i,SV609: $i,SV747: $i] :
( ( ! [SY2403: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2403 @ tc_HOL_Obool ) ) @ SV747 ) @ SV609 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV418 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ SY2403 @ SV418 @ SV180 ) @ SV747 ) ) @ ( hAPP @ ( c_Set_Oimage @ SY2403 @ SV418 @ SV180 ) @ SV609 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6593]) ).
thf(6809,plain,
! [SV181: $i,SV419: $i,SV610: $i,SV748: $i] :
( ( ! [SY2404: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2404 @ SV748 @ SV610 ) @ SV419 ) @ SV181 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV610 @ SV181 ) @ SV419 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV610 @ SV181 ) @ SV419 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2404 @ SV748 @ SV610 ) @ SV419 ) @ SV181 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6594]) ).
thf(6810,plain,
! [SV182: $i,SV420: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV420 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV182 ) )
| ( SV420 = SV182 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6595]) ).
thf(6811,plain,
! [SV182: $i,SV420: $i] :
( ( ~ ( ( SV420 != SV182 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV420 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV182 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6595]) ).
thf(6812,plain,
! [SV183: $i,SV421: $i,SV611: $i,SV749: $i] :
( ( ! [SY2405: $i,SY2406: $i,SY2407: $i,SY2408: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2408 @ SY2407 @ SY2406 @ SY2405 ) @ SV749 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV611 @ SY2407 @ SY2406 @ SV421 ) @ SV183 ) )
| ! [SY2409: $i] :
( ( hAPP @ SY2405 @ ( hAPP @ SV749 @ SY2409 ) )
= ( hAPP @ SV421 @ ( hAPP @ SV183 @ SY2409 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6596]) ).
thf(6813,plain,
! [SV184: $i,SV422: $i] :
( ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
| ! [SY1423: $i,SY1424: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1423 ) @ SY1424 ) )
| ( ( hAPP @ SV184 @ SY1423 )
= ( hAPP @ SV184 @ SY1424 ) ) )
| ~ ( ( ( hAPP @ SV184 @ SY1423 )
!= ( hAPP @ SV184 @ SY1424 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1423 ) @ SY1424 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6597]) ).
thf(6814,plain,
! [SV422: $i,SV184: $i] :
( ( ~ ( ~ ! [SY1425: $i,SY1426: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1425 ) @ SY1426 ) )
| ( ( hAPP @ SV184 @ SY1425 )
= ( hAPP @ SV184 @ SY1426 ) ) )
| ~ ( ( ( hAPP @ SV184 @ SY1425 )
!= ( hAPP @ SV184 @ SY1426 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1425 ) @ SY1426 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6597]) ).
thf(6815,plain,
! [SV185: $i,SV423: $i,SV612: $i,SV750: $i] :
( ( ! [SY2410: $i] :
( ( ( hAPP @ SY2410 @ SV750 )
!= SV612 )
| ( ( c_Fun_Ofun__upd @ SV423 @ SV185 @ SY2410 @ SV750 @ SV612 )
= SY2410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6598]) ).
thf(6816,plain,
! [SV186: $i,SV424: $i,SV613: $i,SV751: $i] :
( ( ! [SY2411: $i,SY2412: $i,SY2413: $i,SY2414: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2414 @ SY2413 ) @ SY2412 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2411 @ SY2412 ) @ SV751 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV613 @ SV424 @ SV186 @ SY2414 @ SY2411 ) @ SY2413 ) @ SV751 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6599]) ).
thf(6817,plain,
! [SV187: $i,SV425: $i,SV614: $i,SV752: $i] :
( ( ! [SY2415: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2415 ) @ SV752 ) @ SV614 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2415 ) @ SV425 ) @ SV187 ) )
| ~ ( ( SV752 != SV425 )
| ( SV614 != SV187 ) ) )
| ~ ( ~ ~ ( ( SV752 != SV425 )
| ( SV614 != SV187 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2415 ) @ SV752 ) @ SV614 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2415 ) @ SV425 ) @ SV187 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6600]) ).
thf(6818,plain,
! [SV188: $i,SV426: $i] :
( ( ( SV426 = SV188 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV426 ) @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6601]) ).
thf(6819,plain,
! [SV189: $i,SV427: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV427 ) @ SV189 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV189 ) @ SV427 ) )
| ( SV427 = SV189 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6602]) ).
thf(6820,plain,
! [SV190: $i,SV428: $i,SV615: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV615 @ tc_HOL_Obool ) ) @ SV428 ) @ SV190 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV615 @ tc_HOL_Obool ) ) @ SV190 ) @ SV428 )
= SV190 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6603]) ).
thf(6821,plain,
! [SV191: $i,SV429: $i,SV616: $i,SV753: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SV616 ) @ SV429 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SV429 ) @ SV191 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SV616 ) @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6604]) ).
thf(6822,plain,
! [SV192: $i,SV430: $i,SV617: $i,SV754: $i] :
( ( ! [SY2416: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2416 @ tc_HOL_Obool ) ) @ SV754 ) @ SV617 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2416 @ tc_HOL_Obool ) ) @ SV430 ) @ SV192 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2416 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2416 @ tc_HOL_Obool ) ) @ SV754 ) @ SV192 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2416 @ tc_HOL_Obool ) ) @ SV617 ) @ SV430 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6605]) ).
thf(6823,plain,
! [SV193: $i,SV431: $i,SV618: $i] :
( ( ( SV618 != SV431 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV193 @ tc_HOL_Obool ) ) @ SV618 ) @ SV431 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6606]) ).
thf(6824,plain,
! [SV194: $i,SV432: $i,SV619: $i] :
( ( SV619
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV432 ) @ SV194 ) @ SV619 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6607]) ).
thf(6825,plain,
! [SV195: $i,SV433: $i] :
( ( ( class_Orderings_Obot @ SV433 )
= $false )
| ( ( class_Orderings_Obot @ ( tc_fun @ SV195 @ SV433 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6608]) ).
thf(6826,plain,
! [SV196: $i,SV434: $i,SV620: $i,SV755: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV755 @ tc_HOL_Obool ) ) @ SV620 ) @ SV434 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV755 @ tc_HOL_Obool ) ) @ SV434 ) @ SV196 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV755 @ tc_HOL_Obool ) ) @ SV620 ) @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6609]) ).
thf(6827,plain,
! [SV197: $i,SV435: $i,SV621: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV621 @ SV435 ) @ SV197 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV435 @ SV197 ) @ SV197 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV435 @ SV197 ) @ SV197 ) )
| ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV621 @ SV435 ) @ SV197 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6610]) ).
thf(6828,plain,
! [SV198: $i,SV436: $i,SV622: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV622 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV622 ) @ SV436 ) @ SV198 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV622 ) @ SV198 ) @ SV436 ) )
| ( SV436 = SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6611]) ).
thf(6829,plain,
! [SV199: $i,SV437: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) @ SV199 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) ) )
| ( SV199
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6612]) ).
thf(6830,plain,
! [SV437: $i,SV199: $i] :
( ( ~ ( ( SV199
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) @ SV199 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6612]) ).
thf(6831,plain,
! [SV200: $i,SV438: $i,SV623: $i,SV756: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV756 @ tc_HOL_Obool ) ) @ SV623 ) @ SV438 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV756 @ tc_HOL_Obool ) ) @ SV200 ) @ SV438 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV756 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV756 @ tc_HOL_Obool ) ) @ SV623 ) @ SV200 ) ) @ SV438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6613]) ).
thf(6832,plain,
! [SV201: $i,SV439: $i,SV624: $i,SV757: $i] :
( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV757 @ SV624 @ SV439 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV757 @ SV201 @ SV624 )
| ( c_Hoare__Mirabelle_Ohoare__derivs @ SV757 @ SV201 @ SV439 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6614]) ).
thf(6833,plain,
! [SV202: $i,SV440: $i,SV625: $i] :
( ( ~ ( ~ ! [SY2261: $i] : ( hBOOL @ ( hAPP @ SV625 @ SY2261 ) )
| ! [SY2262: $i,SY2263: $i] : ( hBOOL @ ( hAPP @ SV625 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV202 ) @ SY2262 ) @ SY2263 ) ) ) )
| ~ ( ~ ! [SY2264: $i,SY2265: $i] : ( hBOOL @ ( hAPP @ SV625 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV202 ) @ SY2264 ) @ SY2265 ) ) )
| ! [SY2266: $i] : ( hBOOL @ ( hAPP @ SV625 @ SY2266 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6615]) ).
thf(6834,plain,
! [SV203: $i,SV441: $i,SV626: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV626 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV441 ) @ SV203 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV203 ) @ SV441 ) )
| ( SV203 = SV441 ) )
| ~ ( ( SV203 != SV441 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV203 ) @ SV441 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6616]) ).
thf(6835,plain,
! [SV204: $i,SV442: $i,SV627: $i,SV758: $i] :
( ( ! [SY2417: $i,SY2418: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2418 @ ( tc_fun @ SY2417 @ tc_HOL_Obool ) ) ) @ SV758 ) @ SV627 ) @ SV442 ) @ SV204 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV758 @ SV442 ) @ SV204 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV627 @ SV442 ) @ SV204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6617]) ).
thf(6836,plain,
! [SV205: $i,SV443: $i,SV628: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV628 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SV443 ) @ SV205 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV628 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SV628 @ tc_HOL_Obool ) @ SV443 ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SV628 @ tc_HOL_Obool ) @ SV205 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6618]) ).
thf(6837,plain,
! [SV206: $i,SV444: $i] :
( ( ( class_Orderings_Opreorder @ SV444 )
= $false )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV206 @ SV444 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6619]) ).
thf(6838,plain,
! [SV207: $i,SV445: $i,SV629: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV629 ) )
= $true )
| ( ( ( SV445 != SV207 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV629 ) @ SV445 ) @ SV207 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6620]) ).
thf(6839,plain,
! [SV208: $i,SV446: $i,SV630: $i,SV759: $i] :
( ( ! [SY2419: $i,SY2420: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2420 @ SY2419 ) @ SV759 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV630 @ ( tc_fun @ SV446 @ tc_HOL_Obool ) ) ) @ SY2420 ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV208 @ SY2419 ) @ SV759 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6621]) ).
thf(6840,plain,
! [SV209: $i,SV447: $i,SV631: $i,SV760: $i] :
( ( ! [SY2421: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY2421 @ SV760 @ SV631 )
| ( ( hAPP @ ( hAPP @ SV631 @ SV447 ) @ ( hAPP @ ( hAPP @ SV631 @ SV447 ) @ SV209 ) )
= ( hAPP @ ( hAPP @ SV631 @ SV447 ) @ SV209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6622]) ).
thf(6841,plain,
! [SV210: $i,SV448: $i,SV632: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV632 ) @ SV448 ) @ SV210 )
= SV210 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6623]) ).
thf(6842,plain,
! [SV211: $i,SV449: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV449 )
= $false )
| ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV211 @ SV449 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6624]) ).
thf(6843,plain,
! [SV212: $i,SV450: $i,SV633: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV633 ) @ SV450 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV633 @ tc_HOL_Obool ) ) @ SV212 ) @ SV450 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV633 ) @ SV212 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6625]) ).
thf(6844,plain,
! [SV213: $i,SV451: $i,SV634: $i,SV761: $i] :
( ( ~ ( class_Orderings_Oorder @ SV761 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV761 ) @ SV634 ) @ SV451 ) )
| ( SV634 != SV213 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV761 ) @ SV213 ) @ SV451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6626]) ).
thf(6845,plain,
! [SV214: $i,SV452: $i,SV635: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV635 ) @ SV452 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV452 ) @ SV214 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV635 ) @ SV214 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6627]) ).
thf(6846,plain,
! [SV215: $i,SV453: $i,SV636: $i,SV762: $i] :
( ( ( SV762 != SV636 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV636 ) @ SV215 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV762 ) @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6628]) ).
thf(6847,plain,
! [SV216: $i,SV454: $i,SV637: $i,SV763: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV763 ) @ SV637 ) @ SV454 ) @ SV216 ) )
| ( SV637 = SV216 )
| ( hBOOL @ ( hAPP @ SV454 @ SV216 ) ) )
| ~ ( ~ ( ( SV637 = SV216 )
| ( hBOOL @ ( hAPP @ SV454 @ SV216 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV763 ) @ SV637 ) @ SV454 ) @ SV216 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6629]) ).
thf(6848,plain,
! [SV217: $i,SV455: $i,SV638: $i,SV764: $i] :
( ( ! [SY2422: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2422 ) @ SV764 ) @ SV638 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2422 ) @ SV455 ) @ SV217 ) )
| ~ ! [SY2423: $i] :
~ ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2422 ) @ SV455 ) @ SY2423 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2422 ) @ SY2423 ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2422 ) @ SV764 ) @ SY2423 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2422 ) @ SY2423 ) @ SV217 ) ) ) ) )
| ~ ( ~ ~ ! [SY2424: $i] :
~ ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2422 ) @ SV455 ) @ SY2424 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2422 ) @ SY2424 ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2422 ) @ SV764 ) @ SY2424 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2422 ) @ SY2424 ) @ SV217 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2422 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2422 ) @ SV455 ) @ SV217 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6630]) ).
thf(6849,plain,
! [SV218: $i,SV456: $i] :
( ( ( ~ ( ~ ( class_Finite__Set_Ofinite @ SV456 )
| ~ ( class_Finite__Set_Ofinite @ SV218 ) ) )
= $false )
| ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV456 @ SV218 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6631]) ).
thf(6850,plain,
! [SV219: $i,SV457: $i,SV639: $i,SV765: $i] :
( ( ! [SY2425: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2425 @ SV765 @ SV639 ) @ SV457 ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV639 @ SV219 ) @ SV457 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6632]) ).
thf(6851,plain,
! [SV220: $i,SV458: $i,SV640: $i] :
( ( ( SV640 != SV458 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV220 @ tc_HOL_Obool ) ) @ SV458 ) @ SV640 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6633]) ).
thf(6852,plain,
! [SV221: $i,SV459: $i,SV641: $i,SV766: $i] :
( ( ~ ( c_Equiv__Relations_Oequivp @ SV766 @ SV641 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV641 @ SV459 ) @ SV221 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV641 @ SV221 ) @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6634]) ).
thf(6853,plain,
! [SV222: $i,SV460: $i] :
( ( ( class_Lattices_Oboolean__algebra @ SV460 )
= $false )
| ( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SV222 @ SV460 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6635]) ).
thf(6854,plain,
! [SV223: $i,SV461: $i,SV642: $i,SV767: $i] :
( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV767 @ SV642 @ SV461 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV767 ) @ tc_HOL_Obool ) ) @ SV223 ) @ SV461 ) )
| ( c_Hoare__Mirabelle_Ohoare__derivs @ SV767 @ SV642 @ SV223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6636]) ).
thf(6855,plain,
! [SV224: $i,SV462: $i,SV643: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV643 ) @ SV462 )
!= SV224 )
| ( SV462
= ( hAPP @ ( c_List_Orev @ SV643 ) @ SV224 ) ) )
| ~ ( ( SV462
!= ( hAPP @ ( c_List_Orev @ SV643 ) @ SV224 ) )
| ( ( hAPP @ ( c_List_Orev @ SV643 ) @ SV462 )
= SV224 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6637]) ).
thf(6856,plain,
! [SV225: $i,SV463: $i,SV644: $i,SV768: $i] :
( ( ! [SY2426: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY2426 @ SV768 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV644 ) @ SV463 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV463 ) @ SV225 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV644 ) @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6638]) ).
thf(6857,plain,
! [SV226: $i,SV464: $i,SV645: $i,SV769: $i] :
( ( ! [SY2427: $i,SY2428: $i,SY2429: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY2429 @ SY2428 @ SY2427 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
| ~ ! [SY2430: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SY2430 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2430 ) @ SV226 ) ) ) )
| ~ ( ~ ~ ! [SY2431: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SY2431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2431 ) @ SV226 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY2429 @ SY2428 @ SY2427 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6639]) ).
thf(6858,plain,
! [SV227: $i,SV465: $i,SV646: $i,SV770: $i] :
( ( ! [SY2432: $i,SY2433: $i,SY2434: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY2434 @ SY2433 @ SY2432 @ SV770 @ SV646 @ SV465 )
| ( ( hAPP @ ( hAPP @ SY2432 @ SV227 ) @ SV227 )
= SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6640]) ).
thf(6859,plain,
! [SV228: $i,SV466: $i,SV647: $i,SV771: $i] :
( ( ! [SY2435: $i,SY2436: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2436 @ SY2435 ) @ SV771 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV647 @ ( tc_fun @ SV466 @ tc_HOL_Obool ) ) ) @ SY2436 ) @ SV228 ) @ SY2435 ) @ SV771 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6641]) ).
thf(6860,plain,
! [SV229: $i,SV467: $i,SV648: $i,SV772: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV772 ) @ SV648 ) @ SV467 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV772 @ tc_HOL_Obool ) ) @ SV467 ) @ SV229 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV772 ) @ SV648 ) @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6642]) ).
thf(6861,plain,
! [SV230: $i,SV468: $i,SV649: $i,SV773: $i] :
( ( ~ ( class_Orderings_Oorder @ SV773 )
| ( SV649 != SV468 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV773 ) @ SV230 ) @ SV468 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV773 ) @ SV230 ) @ SV649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6643]) ).
thf(6862,plain,
! [SV231: $i,SV469: $i,SV650: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV650 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV650 ) @ SV469 ) @ SV231 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV650 ) @ SV231 ) @ SV469 ) )
| ( SV231 = SV469 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6644]) ).
thf(6863,plain,
! [SV232: $i,SV470: $i] :
( ( ( class_Orderings_Oorder @ SV470 )
= $false )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV232 @ SV470 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6645]) ).
thf(6864,plain,
! [SV233: $i,SV471: $i,SV651: $i,SV774: $i] :
( ( ! [SY2437: $i,SY2438: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2438 @ SY2437 ) @ SV774 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV651 @ ( tc_fun @ SV471 @ tc_HOL_Obool ) ) ) @ SV233 ) @ SY2438 ) @ SY2437 ) @ SV774 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6646]) ).
thf(6865,plain,
! [SV234: $i,SV472: $i,SV652: $i,SV775: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV775 @ tc_HOL_Obool ) ) @ SV652 ) @ SV472 ) @ SV234 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV652 @ SV234 ) )
| ( hBOOL @ ( hAPP @ SV472 @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6647]) ).
thf(6866,plain,
! [SV235: $i,SV473: $i,SV653: $i,SV776: $i] :
( ( ! [SY2439: $i,SY2440: $i,SY2441: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2441 @ SY2440 @ SY2439 @ SV776 @ SV653 )
| ~ ( ~ ( ( ( hAPP @ SY2439 @ SV473 )
!= ( hAPP @ SY2439 @ SV235 ) )
| ( SV473 = SV235 ) )
| ~ ( ( SV473 != SV235 )
| ( ( hAPP @ SY2439 @ SV473 )
= ( hAPP @ SY2439 @ SV235 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6648]) ).
thf(6867,plain,
! [SV236: $i,SV474: $i,SV654: $i,SV777: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV777 @ tc_HOL_Obool ) ) @ SV654 ) @ SV474 ) @ SV236 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV654 @ SV236 ) )
| ~ ( hBOOL @ ( hAPP @ SV474 @ SV236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6649]) ).
thf(6868,plain,
! [SV237: $i,SV475: $i,SV655: $i] :
( ( ( ~ ( c_Predicate_Oreflp @ SV655 @ SV475 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV475 @ SV237 ) @ SV237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6650]) ).
thf(6869,plain,
! [SV238: $i,SV476: $i,SV656: $i,SV778: $i] :
( ( ! [SY2442: $i,SY2443: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2443 @ SY2442 @ SV778 @ SV656 @ SV476 )
| ( ( hAPP @ SV656 @ ( hAPP @ SV778 @ SV238 ) )
= SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6651]) ).
thf(6870,plain,
! [SV239: $i,SV477: $i] :
( ( ( ~ ! [SY2052: $i] :
~ ( hBOOL @ ( hAPP @ SV477 @ SY2052 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV477 @ ( c_Hilbert__Choice_OEps @ SV239 @ SV477 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6652]) ).
thf(6871,plain,
! [SV240: $i,SV478: $i,SV657: $i,SV779: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV779 @ tc_HOL_Obool ) ) @ SV657 ) @ SV478 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV779 @ tc_HOL_Obool ) ) @ SV657 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV779 ) @ SV240 ) @ SV478 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6653]) ).
thf(6872,plain,
! [SV241: $i,SV479: $i,SV658: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV658 @ tc_HOL_Obool ) ) @ SV479 ) @ SV241 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV658 @ tc_HOL_Obool ) ) @ SV241 ) @ SV479 ) )
| ( SV479 = SV241 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6654]) ).
thf(6873,plain,
! [SV242: $i,SV480: $i,SV659: $i] :
( ( ( ~ ( c_Wellfounded_OwfP @ SV659 @ SV480 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV659 @ ( tc_fun @ SV659 @ tc_HOL_Obool ) ) ) @ SV242 ) @ SV480 ) )
| ( c_Wellfounded_OwfP @ SV659 @ SV242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6655]) ).
thf(6874,plain,
! [SV243: $i,SV481: $i,SV660: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV660 ) )
= $true )
| ( ( ~ ( ~ ( ( SV481 != SV243 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) ) )
| ( SV481 = SV243 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6656]) ).
thf(6875,plain,
! [SV28: $i,SV272: $i,SV500: $i,SV667: $i,SV780: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV780 @ SV667 @ SV500 @ SV272 @ SV28 ) @ SV272 )
= SV28 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6663]) ).
thf(6876,plain,
! [SV33: $i,SV275: $i,SV501: $i,SV668: $i,SV781: $i] :
( ( ! [SY2444: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2444 @ SV781 @ SV668 @ SV501 ) @ SV275 ) @ SV33 )
= ( hAPP @ SV501 @ ( hAPP @ SV275 @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6664]) ).
thf(6877,plain,
! [SV34: $i,SV276: $i,SV502: $i,SV669: $i,SV782: $i] :
( ( ! [SY2445: $i,SY2446: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY2446 @ SY2445 @ SV782 @ SV669 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV502 @ SY2446 @ SV782 @ SV276 ) @ SV34 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV502 @ SY2445 @ SV782 @ ( hAPP @ ( c_Fun_Ocomp @ SY2446 @ SY2445 @ SV502 @ SV669 ) @ SV276 ) ) @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6665]) ).
thf(6878,plain,
! [SV35: $i,SV277: $i,SV503: $i,SV670: $i,SV783: $i] :
( ( ! [SY2447: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2447 @ SV783 @ SV670 @ SV503 ) @ SV277 ) @ SV35 )
= ( hAPP @ SV503 @ ( hAPP @ SV277 @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6666]) ).
thf(6879,plain,
! [SV36: $i,SV278: $i,SV504: $i,SV671: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV671 @ ( tc_fun @ SV504 @ tc_HOL_Obool ) ) ) @ SV278 ) @ SV36 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6667]) ).
thf(6880,plain,
! [SV40: $i,SV282: $i,SV505: $i,SV672: $i,SV784: $i] :
( ( ! [SY2448: $i,SY2449: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2449 @ SY2448 @ SV784 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2449 @ SV672 @ SY2448 ) @ SV505 ) @ SV282 ) ) @ SV40 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2449 @ SV672 @ SV784 ) @ SV505 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV672 @ SY2448 @ SV784 ) @ SV282 ) @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6668]) ).
thf(6881,plain,
! [SV43: $i,SV285: $i,SV508: $i,SV674: $i,SV785: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV785 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV785 @ SV674 ) @ SV508 ) @ SV285 ) ) @ SV508 ) @ SV43 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV785 @ SV674 ) @ SV508 ) @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6670]) ).
thf(6882,plain,
! [SV49: $i,SV290: $i,SV511: $i,SV677: $i,SV786: $i] :
( ( ! [SY2450: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY2450 @ SV786 @ SV677 ) @ SV511 ) @ SV290 ) @ SV49 )
= ( hAPP @ SV511 @ ( hAPP @ SV290 @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6673]) ).
thf(6883,plain,
! [SV50: $i,SV291: $i,SV512: $i,SV678: $i,SV787: $i] :
( ( ! [SY2451: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY2451 @ SV787 @ SV678 ) @ SV512 ) @ SV291 ) @ SV50 )
= ( hAPP @ ( hAPP @ SV512 @ SV50 ) @ SV291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6674]) ).
thf(6884,plain,
! [SV51: $i,SV292: $i,SV513: $i,SV679: $i,SV788: $i] :
( ( ! [SY2452: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY2452 @ SV788 @ SV679 ) @ SV513 ) @ SV292 ) @ SV51 )
= ( hAPP @ ( hAPP @ SV513 @ SV51 ) @ ( hAPP @ SV292 @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6675]) ).
thf(6885,plain,
! [SV55: $i,SV294: $i] :
( ( ( hBOOL @ SV294 )
= $false )
| ( ( ~ ( hBOOL @ SV55 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV294 ) @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6679]) ).
thf(6886,plain,
! [SV60: $i,SV299: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV299 ) @ SV60 ) )
= $false )
| ( ( hBOOL @ SV299 )
= $true )
| ( ( hBOOL @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6684]) ).
thf(6887,plain,
! [SV63: $i,SV302: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV302 ) @ SV63 ) )
= $false )
| ( ( ~ ( hBOOL @ SV302 ) )
= $true )
| ( ( hBOOL @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6686]) ).
thf(6888,plain,
! [SV64: $i,SV303: $i,SV514: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV514 @ tc_HOL_Obool ) ) @ SV303 ) @ SV64 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV514 @ tc_HOL_Obool ) ) @ SV64 ) @ SV303 )
= SV303 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6687]) ).
thf(6889,plain,
! [SV65: $i,SV304: $i,SV515: $i,SV680: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV680 @ SV515 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV304 @ SV515 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV65 @ tc_HOL_Obool ) ) @ SV680 ) @ SV304 ) @ SV515 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6688]) ).
thf(6890,plain,
! [SV66: $i,SV305: $i,SV516: $i,SV681: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV681 @ tc_HOL_Obool ) ) @ SV516 ) @ SV305 ) @ SV66 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV516 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6689]) ).
thf(6891,plain,
! [SV67: $i,SV306: $i,SV517: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 )
= SV67 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6690]) ).
thf(6892,plain,
! [SV67: $i,SV306: $i,SV517: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 )
!= SV67 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6690]) ).
thf(6893,plain,
! [SV68: $i,SV307: $i,SV518: $i] :
( ( ( class_Orderings_Olinorder @ SV518 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV518 ) @ SV307 ) @ SV68 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV518 ) @ SV68 ) @ SV307 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6691]) ).
thf(6894,plain,
! [SV69: $i,SV308: $i,SV519: $i,SV682: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV682 @ SV519 @ SV308 ) @ SV69 ) )
| ~ ! [SY1684: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ SY1684 ) @ SV69 ) ) )
| ~ ( ~ ~ ! [SY1685: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ SY1685 ) @ SV69 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV682 @ SV519 @ SV308 ) @ SV69 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6692]) ).
thf(6895,plain,
! [SV70: $i,SV309: $i] :
( ( ~ ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
| ~ ( ~ ~ ! [SY1062: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1062 ) @ SY1062 ) )
| ~ ! [SY1063: $i,SY1064: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1064 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1064 ) @ SY1064 ) ) )
| ( ( hAPP @ SV70 @ SY1063 )
!= ( hAPP @ SV70 @ SY1064 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1064 ) @ SY1064 ) ) )
| ( ( hAPP @ SV70 @ SY1063 )
!= ( hAPP @ SV70 @ SY1064 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1064 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6693]) ).
thf(6896,plain,
! [SV309: $i,SV70: $i] :
( ( ~ ~ ( ~ ~ ! [SY1065: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1065 ) @ SY1065 ) )
| ~ ! [SY1066: $i,SY1067: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) ) ) ) )
| ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6694]) ).
thf(6897,plain,
! [SV71: $i,SV310: $i,SV520: $i,SV683: $i] :
( ( ( SV683 != SV520 )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV683 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV520 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV520 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV683 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6695]) ).
thf(6898,plain,
! [SV73: $i,SV312: $i,SV521: $i,SV684: $i,SV789: $i] :
( ( ! [SY2453: $i,SY2454: $i,SY2455: $i,SY2456: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2456 @ SY2455 @ SY2454 @ SY2453 ) @ SV789 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV684 @ SY2455 @ SY2454 @ SV521 ) @ SV312 ) )
| ( ( hAPP @ SY2453 @ ( hAPP @ SV789 @ SV73 ) )
= ( hAPP @ SV521 @ ( hAPP @ SV312 @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6697]) ).
thf(6899,plain,
! [SV74: $i,SV313: $i,SV522: $i,SV685: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV685 ) )
= $true )
| ( ( ~ ! [SY2341: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV685 ) @ ( hAPP @ SV522 @ SY2341 ) ) @ ( hAPP @ SV313 @ SY2341 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV74 @ SV685 ) ) @ SV522 ) @ SV313 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6698]) ).
thf(6900,plain,
! [SV75: $i,SV314: $i,SV523: $i,SV686: $i,SV790: $i] :
( ( ! [SY2457: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2457 @ SV790 ) @ SV686 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV523 @ SV790 ) @ SV686 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV314 @ ( tc_fun @ SV75 @ tc_HOL_Obool ) ) ) @ SY2457 ) @ SV523 ) @ SV790 ) @ SV686 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6699]) ).
thf(6901,plain,
! [SV77: $i,SV315: $i,SV524: $i] :
( ( ( SV524 = SV315 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV77 @ tc_HOL_Obool ) ) @ SV524 ) @ SV315 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV77 @ tc_HOL_Obool ) ) @ SV315 ) @ SV524 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6700]) ).
thf(6902,plain,
! [SV78: $i,SV316: $i,SV525: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) @ SV316 ) @ SV78 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV525 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ SV525 @ SV316 ) ) @ ( c_Predicate_OPowp @ SV525 @ SV78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6701]) ).
thf(6903,plain,
! [SV80: $i,SV318: $i,SV526: $i] :
( ( ( c_Equiv__Relations_Oequivp @ SV526 @ SV318 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV318 @ SV80 ) @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6703]) ).
thf(6904,plain,
! [SV82: $i,SV320: $i,SV527: $i,SV687: $i] :
( ( ( ~ ( c_Finite__Set_Ofolding__one__idem @ SV687 @ SV527 @ SV320 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV527 @ SV82 ) @ SV82 )
= SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6705]) ).
thf(6905,plain,
! [SV84: $i,SV322: $i,SV528: $i,SV688: $i,SV791: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV791 @ tc_HOL_Obool ) ) @ SV688 ) @ SV528 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV322 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV322 @ SV791 @ SV84 ) @ SV688 ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV322 @ SV791 @ SV84 ) @ SV528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6707]) ).
thf(6906,plain,
! [SV85: $i,SV323: $i,SV529: $i] :
( ( ( ~ ! [SY2115: $i] :
~ ( hBOOL @ ( hAPP @ SV529 @ SY2115 ) ) )
= $false )
| ( ( ( SV323
!= ( c_Hilbert__Choice_OEps @ SV85 @ SV529 ) )
| ( hBOOL @ ( hAPP @ SV529 @ SV323 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6708]) ).
thf(6907,plain,
! [SV86: $i,SV324: $i,SV530: $i,SV689: $i] :
( ( ( SV689 != SV530 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6709]) ).
thf(6908,plain,
! [SV87: $i,SV325: $i,SV531: $i,SV690: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV690 @ tc_HOL_Obool ) ) @ SV531 ) @ SV325 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV690 @ tc_HOL_Obool ) ) @ SV325 ) @ SV87 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV690 @ tc_HOL_Obool ) ) @ SV531 ) @ SV87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6710]) ).
thf(6909,plain,
! [SV88: $i,SV326: $i,SV532: $i,SV691: $i,SV792: $i] :
( ( ! [SY2458: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2458 @ ( tc_fun @ SV792 @ tc_HOL_Obool ) ) ) @ SV691 ) @ SV532 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV691 @ SV326 ) @ SV88 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV532 @ SV326 ) @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6711]) ).
thf(6910,plain,
! [SV89: $i,SV327: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ SV327 )
!= ( hAPP @ c_Int_ORep__Integ @ SV89 ) )
| ( SV327 = SV89 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6712]) ).
thf(6911,plain,
! [SV89: $i,SV327: $i] :
( ( ( SV327 != SV89 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV327 )
= ( hAPP @ c_Int_ORep__Integ @ SV89 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6713]) ).
thf(6912,plain,
! [SV90: $i,SV328: $i,SV533: $i,SV692: $i,SV793: $i] :
( ( ! [SY2459: $i] :
( ~ ( ( SY2459 != SV793 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV692 @ SV533 @ SV328 @ SV793 @ SV90 ) @ SY2459 )
= ( hAPP @ SV328 @ SY2459 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6714]) ).
thf(6913,plain,
! [SV91: $i,SV329: $i,SV534: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV534 ) @ SV329 )
!= ( hAPP @ ( c_List_Orev @ SV534 ) @ SV91 ) )
| ( SV329 = SV91 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6715]) ).
thf(6914,plain,
! [SV534: $i,SV91: $i,SV329: $i] :
( ( ~ ( ( SV329 != SV91 )
| ( ( hAPP @ ( c_List_Orev @ SV534 ) @ SV329 )
= ( hAPP @ ( c_List_Orev @ SV534 ) @ SV91 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6715]) ).
thf(6915,plain,
! [SV92: $i,SV330: $i,SV535: $i,SV693: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV693 @ SV535 @ SV330 ) @ SV92 ) )
| ~ ! [SY1733: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ SY1733 ) ) )
| ~ ( ~ ~ ! [SY1734: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ SY1734 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV693 @ SV535 @ SV330 ) @ SV92 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6716]) ).
thf(6916,plain,
! [SV93: $i,SV331: $i,SV536: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV536 ) @ tc_HOL_Obool ) ) @ SV331 ) @ SV93 ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV536 @ SV93 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6717]) ).
thf(6917,plain,
! [SV95: $i,SV333: $i,SV537: $i,SV694: $i,SV794: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ SV694 ) @ SV537 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ SV333 ) @ SV95 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ SV694 ) @ SV333 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ SV537 ) @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6719]) ).
thf(6918,plain,
! [SV96: $i,SV334: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV334 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV96 ) )
| ( SV334 = SV96 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6720]) ).
thf(6919,plain,
! [SV96: $i,SV334: $i] :
( ( ( SV334 != SV96 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV334 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV96 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6721]) ).
thf(6920,plain,
! [SV97: $i,SV335: $i,SV538: $i,SV695: $i,SV795: $i] :
( ( ! [SY2460: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2460 @ ( tc_fun @ SV795 @ tc_HOL_Obool ) ) ) @ SV695 ) @ SV538 ) @ SV335 ) @ SV97 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV695 @ SV335 ) @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6722]) ).
thf(6921,plain,
! [SV98: $i,SV336: $i,SV539: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV539 @ tc_HOL_Obool ) ) @ SV336 ) @ SV98 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV539 @ tc_HOL_Obool ) ) @ SV336 ) @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6723]) ).
thf(6922,plain,
! [SV99: $i,SV337: $i,SV540: $i,SV696: $i,SV796: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV796 @ SV696 @ SV540 ) @ SV337 ) @ SV99 ) )
| ( hBOOL @ ( hAPP @ SV337 @ ( hAPP @ SV540 @ SV99 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV337 @ ( hAPP @ SV540 @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV796 @ SV696 @ SV540 ) @ SV337 ) @ SV99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6724]) ).
thf(6923,plain,
! [SV100: $i,SV338: $i,SV541: $i,SV697: $i,SV797: $i] :
( ( ! [SY2461: $i,SY2462: $i,SY2463: $i,SY2464: $i,SY2465: $i,SY2466: $i] :
( ( ( hAPP @ SY2466 @ ( hAPP @ SY2465 @ SY2464 ) )
!= ( hAPP @ SY2463 @ ( hAPP @ SY2462 @ SY2461 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV797 @ SV697 @ SV541 @ SY2466 ) @ SY2465 ) @ SY2464 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV338 @ SV697 @ SV100 @ SY2463 ) @ SY2462 ) @ SY2461 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6725]) ).
thf(6924,plain,
! [SV101: $i,SV339: $i,SV542: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV339 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) @ SV339 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6726]) ).
thf(6925,plain,
! [SV339: $i,SV101: $i,SV542: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) @ SV339 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV339 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6726]) ).
thf(6926,plain,
! [SV102: $i,SV340: $i,SV543: $i,SV698: $i,SV798: $i] :
( ( ! [SY2467: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY2467 @ SV798 @ SV698 )
| ( ( hAPP @ ( hAPP @ SV698 @ SV543 ) @ ( hAPP @ ( hAPP @ SV698 @ SV340 ) @ SV102 ) )
= ( hAPP @ ( hAPP @ SV698 @ SV340 ) @ ( hAPP @ ( hAPP @ SV698 @ SV543 ) @ SV102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6727]) ).
thf(6927,plain,
! [SV103: $i,SV341: $i,SV544: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV103 ) )
| ! [SY2145: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SY2145 ) @ SV103 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SY2145 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6728]) ).
thf(6928,plain,
! [SV544: $i,SV103: $i,SV341: $i] :
( ( ~ ( ~ ! [SY2146: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SY2146 ) @ SV103 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SY2146 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV103 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6728]) ).
thf(6929,plain,
! [SV104: $i,SV342: $i,SV545: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV545 @ tc_HOL_Obool ) ) @ SV342 ) @ SV104 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV545 @ tc_HOL_Obool ) ) @ SV342 ) @ SV104 )
= SV342 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6729]) ).
thf(6930,plain,
! [SV105: $i,SV343: $i,SV546: $i,SV699: $i,SV799: $i] :
( ( ~ ( c_Equiv__Relations_Opart__equivp @ SV799 @ SV699 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV546 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV343 ) @ SV105 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV546 ) @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6730]) ).
thf(6931,plain,
! [SV108: $i,SV346: $i] :
( ( ( ! [SY1768: $i] :
~ ( hBOOL @ ( hAPP @ SV346 @ SY1768 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV346 @ ( c_Hilbert__Choice_OEps @ SV108 @ SV346 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6733]) ).
thf(6932,plain,
! [SV109: $i,SV347: $i,SV547: $i,SV700: $i,SV800: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV800 @ SV700 ) @ SV547 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV347 @ SV109 @ SV800 ) @ SV547 ) @ SV700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6734]) ).
thf(6933,plain,
! [SV110: $i,SV348: $i,SV548: $i,SV701: $i,SV801: $i] :
( ( ~ ( ~ ( ( ( c_Fun_Ofun__upd @ SV801 @ SV701 @ SV548 @ SV348 @ SV110 )
!= SV548 )
| ( ( hAPP @ SV548 @ SV348 )
= SV110 ) )
| ~ ( ( ( hAPP @ SV548 @ SV348 )
!= SV110 )
| ( ( c_Fun_Ofun__upd @ SV801 @ SV701 @ SV548 @ SV348 @ SV110 )
= SV548 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6735]) ).
thf(6934,plain,
! [SV111: $i,SV349: $i,SV549: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV549 @ tc_HOL_Obool ) ) @ SV349 ) @ SV111 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV549 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ SV549 ) @ SV349 ) ) @ ( hAPP @ ( c_Set_OPow @ SV549 ) @ SV111 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6736]) ).
thf(6935,plain,
! [SV112: $i,SV350: $i,SV550: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV112 ) )
| ! [SY2153: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV350 @ SY2153 ) @ SV112 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SY2153 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6737]) ).
thf(6936,plain,
! [SV550: $i,SV112: $i,SV350: $i] :
( ( ~ ( ~ ! [SY2154: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV350 @ SY2154 ) @ SV112 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SY2154 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV112 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6737]) ).
thf(6937,plain,
! [SV113: $i,SV351: $i,SV551: $i,SV702: $i] :
( ( ( ~ ( c_Predicate_Osymp @ SV702 @ SV551 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV551 @ SV351 ) @ SV113 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV551 @ SV113 ) @ SV351 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6738]) ).
thf(6938,plain,
! [SV114: $i,SV352: $i,SV552: $i,SV703: $i,SV802: $i] :
( ( ! [SY2468: $i] :
~ ( ~ ( ( SY2468 != SV802 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV703 @ SV552 @ SV352 @ SV802 @ SV114 ) @ SY2468 )
= SV114 ) )
| ~ ( ~ ( ( SY2468 != SV802 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV703 @ SV552 @ SV352 @ SV802 @ SV114 ) @ SY2468 )
= ( hAPP @ SV352 @ SY2468 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6739]) ).
thf(6939,plain,
! [SV115: $i,SV353: $i,SV553: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV553 @ tc_HOL_Obool ) ) @ SV353 ) @ SV115 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV553 ) @ SV115 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV553 ) @ SV353 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6740]) ).
thf(6940,plain,
! [SV116: $i,SV354: $i] :
( ( ( ~ ( class_Enum_Oenum @ SV354 )
| ~ ( class_Enum_Oenum @ SV116 ) )
= $true )
| ( ( class_Enum_Oenum @ ( tc_fun @ SV354 @ SV116 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6741]) ).
thf(6941,plain,
! [SV117: $i,SV355: $i,SV554: $i,SV704: $i,SV803: $i] :
( ( ! [SY2469: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2469 @ SV803 ) @ SV704 ) @ SV554 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2469 @ SV803 ) @ SV355 ) @ SV117 ) )
| ~ ( ( SV704 != SV355 )
| ( SV554 != SV117 ) ) )
| ~ ( ~ ~ ( ( SV704 != SV355 )
| ( SV554 != SV117 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2469 @ SV803 ) @ SV704 ) @ SV554 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2469 @ SV803 ) @ SV355 ) @ SV117 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6742]) ).
thf(6942,plain,
! [SV356: $i,SV118: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV118 ) @ SV356 ) ) )
= $true )
| ( ( SV356 = SV118 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV356 ) @ SV118 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6743]) ).
thf(6943,plain,
! [SV119: $i,SV357: $i,SV555: $i,SV705: $i,SV804: $i] :
( ( ! [SY2470: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2470 @ ( tc_fun @ SV804 @ tc_HOL_Obool ) ) ) @ SV705 ) @ SV555 ) @ SV357 ) @ SV119 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV555 @ SV357 ) @ SV119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6744]) ).
thf(6944,plain,
! [SV120: $i,SV358: $i,SV556: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
| ( SV358 = SV120 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6745]) ).
thf(6945,plain,
! [SV120: $i,SV358: $i,SV556: $i] :
( ( ~ ( ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
| ( SV358 = SV120 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6745]) ).
thf(6946,plain,
! [SV121: $i,SV359: $i,SV557: $i,SV706: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV706 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV557 @ SV706 ) ) @ SV359 ) @ SV121 ) )
| ! [SY2373: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV706 ) @ ( hAPP @ SV359 @ SY2373 ) ) @ ( hAPP @ SV121 @ SY2373 ) ) ) )
| ~ ( ~ ! [SY2374: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV706 ) @ ( hAPP @ SV359 @ SY2374 ) ) @ ( hAPP @ SV121 @ SY2374 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV557 @ SV706 ) ) @ SV359 ) @ SV121 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6746]) ).
thf(6947,plain,
! [SV122: $i,SV360: $i,SV558: $i] :
( ( ( hBOOL @ ( hAPP @ SV558 @ SV360 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV558 @ ( c_Hilbert__Choice_OEps @ SV122 @ SV558 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6747]) ).
thf(6948,plain,
! [SV123: $i,SV361: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV361 @ ( c_Hilbert__Choice_OEps @ SV123 @ SV361 ) ) )
| ~ ! [SY1800: $i] :
~ ( hBOOL @ ( hAPP @ SV361 @ SY1800 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6748]) ).
thf(6949,plain,
! [SV123: $i,SV361: $i] :
( ( ~ ~ ! [SY1801: $i] :
~ ( hBOOL @ ( hAPP @ SV361 @ SY1801 ) )
| ( hBOOL @ ( hAPP @ SV361 @ ( c_Hilbert__Choice_OEps @ SV123 @ SV361 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6749]) ).
thf(6950,plain,
! [SV124: $i,SV362: $i] :
( ( ( ( hAPP @ SV362 @ ( sK2_SY1802 @ SV124 @ SV362 ) )
= ( hAPP @ SV124 @ ( sK2_SY1802 @ SV124 @ SV362 ) ) )
= $false )
| ( ( SV362 = SV124 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6750]) ).
thf(6951,plain,
! [SV125: $i,SV363: $i,SV559: $i,SV707: $i,SV805: $i] :
( ( ~ ( c_Fun_Oinj__on @ SV805 @ SV707 @ SV559 @ SV363 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV805 @ tc_HOL_Obool ) ) @ SV125 ) @ SV363 ) )
| ( c_Fun_Oinj__on @ SV805 @ SV707 @ SV559 @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6751]) ).
thf(6952,plain,
! [SV126: $i,SV364: $i,SV560: $i,SV708: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV708 ) )
= $true )
| ( ( ( SV560 != SV364 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV708 ) @ SV364 ) @ SV126 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV708 ) @ SV560 ) @ SV126 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6752]) ).
thf(6953,plain,
! [SV127: $i,SV365: $i,SV561: $i,SV709: $i,SV806: $i] :
( ( ! [SY2471: $i,SY2472: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2472 @ SY2471 @ SV806 @ SV709 ) @ SV561 )
!= SV365 )
| ( ( hAPP @ SV709 @ ( hAPP @ SV561 @ SV127 ) )
= ( hAPP @ SV365 @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6753]) ).
thf(6954,plain,
! [SV128: $i,SV366: $i,SV562: $i,SV710: $i,SV807: $i] :
( ( ! [SY2473: $i] :
~ ( ~ ( ( SY2473 != SV807 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV710 @ SV562 @ SV366 @ SV807 @ SV128 ) @ SY2473 )
= SV128 ) )
| ~ ( ~ ( ( SY2473 != SV807 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV710 @ SV562 @ SV366 @ SV807 @ SV128 ) @ SY2473 )
= ( hAPP @ SV366 @ SY2473 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6754]) ).
thf(6955,plain,
! [SV129: $i,SV367: $i,SV563: $i,SV711: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV367 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV129 ) )
| ( SV367 = SV129 ) )
| ~ ( ( SV367 != SV129 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV367 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV129 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6755]) ).
thf(6956,plain,
! [SV130: $i,SV368: $i,SV564: $i,SV712: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV712 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV712 ) @ SV564 ) @ SV368 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV712 ) @ SV368 ) @ SV130 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV712 ) @ SV564 ) @ SV130 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6756]) ).
thf(6957,plain,
! [SV131: $i,SV369: $i,SV565: $i,SV713: $i] :
( ( ( SV713 != SV565 )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV713 ) @ SV131 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV565 ) @ SV131 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV565 ) @ SV131 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV713 ) @ SV131 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6757]) ).
thf(6958,plain,
! [SV132: $i,SV370: $i,SV566: $i,SV714: $i,SV808: $i] :
( ( ! [SY2474: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2474 ) @ SV808 ) @ SV714 )
!= SV566 )
| ( SV370
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2474 ) @ SV714 ) @ SV132 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2474 ) @ SV808 ) @ SV370 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2474 ) @ SV566 ) @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6758]) ).
thf(6959,plain,
! [SV133: $i,SV371: $i,SV567: $i,SV715: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV567 ) @ SV371 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV133 ) @ SV371 ) )
| ( SV567 = SV133 ) )
| ~ ( ( SV567 != SV133 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV567 ) @ SV371 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV133 ) @ SV371 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6759]) ).
thf(6960,plain,
! [SV134: $i,SV372: $i,SV568: $i,SV716: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV716 @ tc_HOL_Obool ) ) @ SV568 ) @ SV372 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV568 @ SV134 ) )
| ( hBOOL @ ( hAPP @ SV372 @ SV134 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6760]) ).
thf(6961,plain,
! [SV135: $i,SV373: $i,SV569: $i,SV717: $i] :
( ( ( ~ ( c_Equiv__Relations_Opart__equivp @ SV717 @ SV569 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV569 @ SV373 ) @ SV135 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV569 @ SV135 ) @ SV373 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6761]) ).
thf(6962,plain,
! [SV136: $i,SV374: $i,SV570: $i,SV718: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV718 @ SV570 ) @ SV374 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV718 @ SV570 ) @ SV136 ) )
| ( SV374 = SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6762]) ).
thf(6963,plain,
! [SV137: $i,SV375: $i,SV571: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV571 ) @ SV375 ) @ SV137 ) )
| ( hBOOL @ ( hAPP @ SV137 @ SV375 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6763]) ).
thf(6964,plain,
! [SV571: $i,SV375: $i,SV137: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV137 @ SV375 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV571 ) @ SV375 ) @ SV137 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6763]) ).
thf(6965,plain,
! [SV138: $i,SV376: $i,SV572: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV572 @ ( tc_fun @ SV572 @ tc_HOL_Obool ) ) ) @ SV376 ) @ SV138 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV572 @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ SV572 @ SV138 ) ) @ ( c_Wellfounded_Oaccp @ SV572 @ SV376 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6764]) ).
thf(6966,plain,
! [SV139: $i,SV377: $i,SV573: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV573 @ tc_HOL_Obool ) ) @ SV377 ) @ SV139 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV573 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV573 @ tc_HOL_Obool ) ) @ SV139 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV573 @ tc_HOL_Obool ) ) @ SV377 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6765]) ).
thf(6967,plain,
! [SV140: $i,SV378: $i,SV574: $i,SV719: $i,SV809: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV809 @ SV719 ) @ SV574 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV378 @ SV140 @ SV809 ) @ SV574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6766]) ).
thf(6968,plain,
! [SV141: $i,SV379: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV379 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV141 ) )
| ( SV379 = SV141 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6767]) ).
thf(6969,plain,
! [SV141: $i,SV379: $i] :
( ( ( SV379 != SV141 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV379 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV141 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6768]) ).
thf(6970,plain,
! [SV142: $i,SV380: $i,SV575: $i,SV720: $i,SV810: $i] :
( ( ! [SY2475: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2475 @ ( tc_fun @ SV810 @ tc_HOL_Obool ) ) ) @ SV720 ) @ SV575 ) @ SV380 ) @ SV142 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV720 @ SV380 ) @ SV142 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV575 @ SV380 ) @ SV142 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6769]) ).
thf(6971,plain,
! [SV143: $i,SV381: $i,SV576: $i,SV721: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV576 ) @ SV381 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV576 ) @ SV143 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV576 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV381 ) @ SV143 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6770]) ).
thf(6972,plain,
! [SV144: $i,SV382: $i,SV577: $i] :
( ( ~ ( ( SV577 != SV382 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV577 ) @ SV382 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV382 ) @ SV577 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6771]) ).
thf(6973,plain,
! [SV382: $i,SV577: $i,SV144: $i] :
( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV577 ) @ SV382 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV382 ) @ SV577 ) ) )
| ( SV577 = SV382 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6771]) ).
thf(6974,plain,
! [SV145: $i,SV383: $i,SV578: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV578 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SV383 ) @ SV145 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV578 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SV578 @ tc_HOL_Obool ) @ SV145 ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SV578 @ tc_HOL_Obool ) @ SV383 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6772]) ).
thf(6975,plain,
! [SV146: $i,SV384: $i,SV579: $i,SV722: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV722 @ SV579 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV384 @ tc_HOL_Obool ) ) @ SV722 ) @ SV146 ) )
| ( hBOOL @ ( hAPP @ SV146 @ SV579 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6773]) ).
thf(6976,plain,
! [SV147: $i,SV385: $i,SV580: $i,SV723: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV723 @ tc_HOL_Obool ) ) @ SV580 ) @ SV385 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV723 @ tc_HOL_Obool ) ) @ SV385 ) @ SV147 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV723 @ tc_HOL_Obool ) ) @ SV580 ) @ SV147 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6774]) ).
thf(6977,plain,
! [SV148: $i,SV386: $i,SV581: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV581 ) @ SV386 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV386 ) @ SV148 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV581 ) @ SV148 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6775]) ).
thf(6978,plain,
! [SV149: $i,SV387: $i,SV582: $i,SV724: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV724 @ SV582 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV387 @ tc_HOL_Obool ) ) @ SV724 ) @ SV149 ) @ SV582 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6776]) ).
thf(6979,plain,
! [SV150: $i,SV388: $i,SV583: $i,SV725: $i,SV811: $i] :
( ( ~ ( class_Orderings_Oord @ SV811 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV725 @ SV811 ) ) @ SV583 ) @ SV388 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV811 ) @ ( hAPP @ SV583 @ SV150 ) ) @ ( hAPP @ SV388 @ SV150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6777]) ).
thf(6980,plain,
! [SV151: $i,SV389: $i,SV584: $i,SV726: $i,SV812: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV812 @ SV726 ) @ SV584 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV389 @ SV151 @ SV812 ) @ SV726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6778]) ).
thf(6981,plain,
! [SV152: $i,SV390: $i,SV585: $i,SV727: $i,SV813: $i] :
( ( ! [SY2476: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2476 @ SV813 ) @ SV727 ) @ SV585 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2476 @ SV813 ) @ SV390 ) @ SV152 ) )
| ~ ( ( SV727 != SV390 )
| ( SV585 != SV152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6779]) ).
thf(6982,plain,
! [SV153: $i,SV391: $i,SV586: $i,SV728: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV728 @ tc_HOL_Obool ) ) @ SV586 ) @ SV391 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV728 ) @ SV153 ) @ SV586 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV728 ) @ SV153 ) @ SV391 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6780]) ).
thf(6983,plain,
! [SV154: $i,SV392: $i,SV587: $i,SV729: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV729 @ tc_HOL_Obool ) ) @ SV587 ) @ SV392 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV729 ) @ SV154 ) @ SV587 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV729 ) @ SV154 ) @ SV392 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6781]) ).
thf(6984,plain,
! [SV155: $i,SV393: $i,SV588: $i,SV730: $i,SV814: $i] :
( ( ! [SY2477: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2477 @ SV814 ) @ SV730 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV588 @ SV814 ) @ SV730 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV393 @ ( tc_fun @ SV155 @ tc_HOL_Obool ) ) ) @ SV588 ) @ SY2477 ) @ SV814 ) @ SV730 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6782]) ).
thf(6985,plain,
! [SV156: $i,SV394: $i,SV589: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
| ~ ( ( SV394 != SV156 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6783]) ).
thf(6986,plain,
! [SV156: $i,SV394: $i,SV589: $i] :
( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
| ~ ( ( SV394 != SV156 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6783]) ).
thf(6987,plain,
! [SV157: $i,SV395: $i,SV590: $i,SV731: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV731 @ tc_HOL_Obool ) ) @ SV590 ) @ SV395 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV731 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV731 ) @ SV157 ) @ SV590 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV731 ) @ SV157 ) @ SV395 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6784]) ).
thf(6988,plain,
! [SV159: $i,SV397: $i,SV591: $i,SV732: $i,SV815: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV815 @ SV732 @ SV591 ) @ SV397 ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV591 @ SV159 ) @ SV397 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV591 @ SV159 ) @ SV397 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV815 @ SV732 @ SV591 ) @ SV397 ) @ SV159 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6786]) ).
thf(6989,plain,
! [SV160: $i,SV398: $i,SV592: $i,SV733: $i,SV816: $i] :
( ( ~ ( c_Predicate_Otransp @ SV816 @ SV733 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV592 ) @ SV398 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV398 ) @ SV160 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV592 ) @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6787]) ).
thf(6990,plain,
! [SV161: $i,SV399: $i,SV593: $i] :
( ( ~ ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV399 )
!= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV161 ) )
| ( SV399 = SV161 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6788]) ).
thf(6991,plain,
! [SV593: $i,SV161: $i,SV399: $i] :
( ( ~ ( ( SV399 != SV161 )
| ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV399 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV161 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6788]) ).
thf(6992,plain,
! [SV162: $i,SV400: $i,SV594: $i,SV734: $i,SV817: $i] :
( ( ~ ( class_Orderings_Oord @ SV817 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV734 @ SV817 ) ) @ SV594 ) @ SV400 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV817 ) @ ( hAPP @ SV594 @ SV162 ) ) @ ( hAPP @ SV400 @ SV162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6789]) ).
thf(6993,plain,
! [SV163: $i,SV401: $i,SV595: $i,SV735: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV735 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV735 ) @ SV595 ) @ SV401 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV735 ) @ SV163 ) @ SV595 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV735 ) @ SV163 ) @ SV401 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6790]) ).
thf(6994,plain,
! [SV164: $i,SV402: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV402 )
!= ( hAPP @ c_Nat_OSuc @ SV164 ) )
| ( SV402 = SV164 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6791]) ).
thf(6995,plain,
! [SV164: $i,SV402: $i] :
( ( ( SV402 != SV164 )
| ( ( hAPP @ c_Nat_OSuc @ SV402 )
= ( hAPP @ c_Nat_OSuc @ SV164 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6792]) ).
thf(6996,plain,
! [SV165: $i,SV403: $i,SV596: $i,SV736: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV736 @ SV596 ) @ SV403 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV596 @ SV165 ) @ SV403 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV736 @ SV596 ) @ SV165 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6793]) ).
thf(6997,plain,
! [SV166: $i,SV404: $i,SV597: $i,SV737: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV737 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV737 ) @ SV597 ) @ SV404 ) )
| ( SV404 != SV166 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV737 ) @ SV597 ) @ SV166 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6794]) ).
thf(6998,plain,
! [SV167: $i,SV405: $i,SV598: $i,SV738: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV738 @ tc_HOL_Obool ) ) @ SV598 ) @ SV405 ) @ SV167 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV405 @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6795]) ).
thf(6999,plain,
! [SV168: $i,SV406: $i,SV599: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV599 @ tc_HOL_Obool ) ) @ SV406 ) @ SV168 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV599 @ tc_HOL_Obool ) ) @ SV406 ) @ SV168 )
= SV168 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6796]) ).
thf(7000,plain,
! [SV169: $i,SV407: $i,SV600: $i,SV739: $i,SV818: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
| ~ ! [SY2478: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SY2478 ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SY2478 ) ) ) )
| ~ ( ~ ~ ! [SY2479: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SY2479 ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SY2479 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6797]) ).
thf(7001,plain,
! [SV170: $i,SV408: $i,SV601: $i,SV740: $i,SV819: $i] :
( ( ! [SY2480: $i] :
( ( SY2480 != SV819 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV740 @ SV601 @ SV408 ) @ SV170 ) @ SY2480 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV740 @ SV601 @ SV408 ) @ SV170 ) @ SV819 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6798]) ).
thf(7002,plain,
! [SV171: $i,SV409: $i,SV602: $i,SV741: $i] :
( ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV741 @ SV602 ) )
| ( hBOOL @ ( hAPP @ SV409 @ SV602 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV171 @ tc_HOL_Obool ) ) @ SV409 ) @ SV741 ) @ SV602 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6799]) ).
thf(7003,plain,
! [SV172: $i,SV410: $i,SV603: $i,SV742: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV742 @ tc_HOL_Obool ) ) @ SV603 ) @ SV410 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV742 @ tc_HOL_Obool ) ) @ SV410 ) @ SV172 ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV742 @ tc_HOL_Obool ) ) @ SV410 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV742 @ tc_HOL_Obool ) ) @ SV172 ) @ SV603 ) )
= SV603 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6800]) ).
thf(7004,plain,
! [SV173: $i,SV411: $i,SV604: $i] :
( ( ( class_Orderings_Olinorder @ SV604 )
= $false )
| ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV604 ) @ SV411 ) @ SV173 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV604 ) @ SV173 ) @ SV411 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6801]) ).
thf(7005,plain,
! [SV174: $i,SV412: $i,SV605: $i,SV743: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV743 @ SV605 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV412 @ tc_HOL_Obool ) ) @ SV174 ) @ SV743 ) @ SV605 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6802]) ).
thf(7006,plain,
! [SV177: $i,SV415: $i,SV606: $i,SV744: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV744 @ tc_HOL_Obool ) ) @ SV606 ) @ SV415 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV744 ) @ SV177 ) @ SV606 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV744 ) @ SV177 ) @ SV415 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6805]) ).
thf(7007,plain,
! [SV178: $i,SV416: $i,SV607: $i,SV745: $i,SV820: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV745 ) @ SV607 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV416 ) @ SV178 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV745 ) @ SV416 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV607 ) @ SV178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6806]) ).
thf(7008,plain,
! [SV179: $i,SV417: $i,SV608: $i,SV746: $i,SV821: $i] :
( ( ! [SY2481: $i] :
( ~ ( ( SY2481 != SV821 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ SV608 ) @ SY2481 ) @ SV417 ) ) @ SV821 ) @ SV179 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ SV608 ) @ SV821 ) @ SV179 ) ) @ SY2481 ) @ SV417 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6807]) ).
thf(7009,plain,
! [SV180: $i,SV418: $i,SV609: $i,SV747: $i,SV822: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV747 ) @ SV609 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV418 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ SV822 @ SV418 @ SV180 ) @ SV747 ) ) @ ( hAPP @ ( c_Set_Oimage @ SV822 @ SV418 @ SV180 ) @ SV609 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6808]) ).
thf(7010,plain,
! [SV181: $i,SV419: $i,SV610: $i,SV748: $i,SV823: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV823 @ SV748 @ SV610 ) @ SV419 ) @ SV181 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV610 @ SV181 ) @ SV419 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV610 @ SV181 ) @ SV419 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV823 @ SV748 @ SV610 ) @ SV419 ) @ SV181 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6809]) ).
thf(7011,plain,
! [SV182: $i,SV420: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV420 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV182 ) )
| ( SV420 = SV182 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6810]) ).
thf(7012,plain,
! [SV182: $i,SV420: $i] :
( ( ( SV420 != SV182 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV420 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV182 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6811]) ).
thf(7013,plain,
! [SV183: $i,SV421: $i,SV611: $i,SV749: $i,SV824: $i] :
( ( ! [SY2482: $i,SY2483: $i,SY2484: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2484 @ SY2483 @ SY2482 @ SV824 ) @ SV749 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV611 @ SY2483 @ SY2482 @ SV421 ) @ SV183 ) )
| ! [SY2485: $i] :
( ( hAPP @ SV824 @ ( hAPP @ SV749 @ SY2485 ) )
= ( hAPP @ SV421 @ ( hAPP @ SV183 @ SY2485 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6812]) ).
thf(7014,plain,
! [SV184: $i,SV422: $i] :
( ( ~ ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
| ! [SY1423: $i,SY1424: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1423 ) @ SY1424 ) )
| ( ( hAPP @ SV184 @ SY1423 )
= ( hAPP @ SV184 @ SY1424 ) ) )
| ~ ( ( ( hAPP @ SV184 @ SY1423 )
!= ( hAPP @ SV184 @ SY1424 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1423 ) @ SY1424 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6813]) ).
thf(7015,plain,
! [SV422: $i,SV184: $i] :
( ( ~ ! [SY1425: $i,SY1426: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1425 ) @ SY1426 ) )
| ( ( hAPP @ SV184 @ SY1425 )
= ( hAPP @ SV184 @ SY1426 ) ) )
| ~ ( ( ( hAPP @ SV184 @ SY1425 )
!= ( hAPP @ SV184 @ SY1426 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1425 ) @ SY1426 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6814]) ).
thf(7016,plain,
! [SV185: $i,SV423: $i,SV612: $i,SV750: $i,SV825: $i] :
( ( ( ( hAPP @ SV825 @ SV750 )
!= SV612 )
| ( ( c_Fun_Ofun__upd @ SV423 @ SV185 @ SV825 @ SV750 @ SV612 )
= SV825 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6815]) ).
thf(7017,plain,
! [SV186: $i,SV424: $i,SV613: $i,SV751: $i,SV826: $i] :
( ( ! [SY2486: $i,SY2487: $i,SY2488: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2488 @ SY2487 ) @ SY2486 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV826 @ SY2486 ) @ SV751 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV613 @ SV424 @ SV186 @ SY2488 @ SV826 ) @ SY2487 ) @ SV751 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6816]) ).
thf(7018,plain,
! [SV187: $i,SV425: $i,SV614: $i,SV752: $i,SV827: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV752 ) @ SV614 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV425 ) @ SV187 ) )
| ~ ( ( SV752 != SV425 )
| ( SV614 != SV187 ) ) )
| ~ ( ~ ~ ( ( SV752 != SV425 )
| ( SV614 != SV187 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV752 ) @ SV614 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV425 ) @ SV187 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6817]) ).
thf(7019,plain,
! [SV427: $i,SV189: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV189 ) @ SV427 ) ) )
= $true )
| ( ( SV427 = SV189 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV427 ) @ SV189 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6819]) ).
thf(7020,plain,
! [SV190: $i,SV428: $i,SV615: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV615 @ tc_HOL_Obool ) ) @ SV428 ) @ SV190 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV615 @ tc_HOL_Obool ) ) @ SV190 ) @ SV428 )
= SV190 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6820]) ).
thf(7021,plain,
! [SV191: $i,SV429: $i,SV616: $i,SV753: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SV616 ) @ SV429 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SV429 ) @ SV191 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SV616 ) @ SV191 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6821]) ).
thf(7022,plain,
! [SV192: $i,SV430: $i,SV617: $i,SV754: $i,SV828: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ SV754 ) @ SV617 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ SV430 ) @ SV192 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ SV754 ) @ SV192 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ SV617 ) @ SV430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6822]) ).
thf(7023,plain,
! [SV193: $i,SV431: $i,SV618: $i] :
( ( ( SV618 = SV431 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV193 @ tc_HOL_Obool ) ) @ SV618 ) @ SV431 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6823]) ).
thf(7024,plain,
! [SV196: $i,SV434: $i,SV620: $i,SV755: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV755 @ tc_HOL_Obool ) ) @ SV620 ) @ SV434 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV755 @ tc_HOL_Obool ) ) @ SV434 ) @ SV196 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV755 @ tc_HOL_Obool ) ) @ SV620 ) @ SV196 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6826]) ).
thf(7025,plain,
! [SV197: $i,SV435: $i,SV621: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV621 @ SV435 ) @ SV197 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV435 @ SV197 ) @ SV197 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6827]) ).
thf(7026,plain,
! [SV621: $i,SV197: $i,SV435: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV435 @ SV197 ) @ SV197 ) )
| ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV621 @ SV435 ) @ SV197 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6827]) ).
thf(7027,plain,
! [SV198: $i,SV436: $i,SV622: $i] :
( ( ( class_Orderings_Oorder @ SV622 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV622 ) @ SV436 ) @ SV198 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV622 ) @ SV198 ) @ SV436 ) )
| ( SV436 = SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6828]) ).
thf(7028,plain,
! [SV199: $i,SV437: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) @ SV199 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) ) )
| ( SV199
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6829]) ).
thf(7029,plain,
! [SV437: $i,SV199: $i] :
( ( ( SV199
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) @ SV199 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6830]) ).
thf(7030,plain,
! [SV200: $i,SV438: $i,SV623: $i,SV756: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV756 @ tc_HOL_Obool ) ) @ SV623 ) @ SV438 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV756 @ tc_HOL_Obool ) ) @ SV200 ) @ SV438 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV756 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV756 @ tc_HOL_Obool ) ) @ SV623 ) @ SV200 ) ) @ SV438 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6831]) ).
thf(7031,plain,
! [SV201: $i,SV439: $i,SV624: $i,SV757: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV757 @ SV624 @ SV439 ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV757 @ SV201 @ SV624 )
| ( c_Hoare__Mirabelle_Ohoare__derivs @ SV757 @ SV201 @ SV439 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6832]) ).
thf(7032,plain,
! [SV202: $i,SV440: $i,SV625: $i] :
( ( ~ ( ~ ! [SY2261: $i] : ( hBOOL @ ( hAPP @ SV625 @ SY2261 ) )
| ! [SY2262: $i,SY2263: $i] : ( hBOOL @ ( hAPP @ SV625 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV202 ) @ SY2262 ) @ SY2263 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6833]) ).
thf(7033,plain,
! [SV202: $i,SV440: $i,SV625: $i] :
( ( ~ ( ~ ! [SY2264: $i,SY2265: $i] : ( hBOOL @ ( hAPP @ SV625 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV202 ) @ SY2264 ) @ SY2265 ) ) )
| ! [SY2266: $i] : ( hBOOL @ ( hAPP @ SV625 @ SY2266 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6833]) ).
thf(7034,plain,
! [SV203: $i,SV441: $i,SV626: $i] :
( ( ( class_Orderings_Oorder @ SV626 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV441 ) @ SV203 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV203 ) @ SV441 ) )
| ( SV203 = SV441 ) )
| ~ ( ( SV203 != SV441 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV203 ) @ SV441 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6834]) ).
thf(7035,plain,
! [SV204: $i,SV442: $i,SV627: $i,SV758: $i,SV829: $i] :
( ( ! [SY2489: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2489 @ ( tc_fun @ SV829 @ tc_HOL_Obool ) ) ) @ SV758 ) @ SV627 ) @ SV442 ) @ SV204 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV758 @ SV442 ) @ SV204 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV627 @ SV442 ) @ SV204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6835]) ).
thf(7036,plain,
! [SV205: $i,SV443: $i,SV628: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV628 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SV443 ) @ SV205 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV628 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SV628 @ tc_HOL_Obool ) @ SV443 ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SV628 @ tc_HOL_Obool ) @ SV205 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6836]) ).
thf(7037,plain,
! [SV207: $i,SV445: $i,SV629: $i] :
( ( ( class_Orderings_Opreorder @ SV629 )
= $false )
| ( ( ( SV445 != SV207 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV629 ) @ SV445 ) @ SV207 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6838]) ).
thf(7038,plain,
! [SV208: $i,SV446: $i,SV630: $i,SV759: $i,SV830: $i] :
( ( ! [SY2490: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2490 @ SV830 ) @ SV759 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV630 @ ( tc_fun @ SV446 @ tc_HOL_Obool ) ) ) @ SY2490 ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV208 @ SV830 ) @ SV759 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6839]) ).
thf(7039,plain,
! [SV209: $i,SV447: $i,SV631: $i,SV760: $i,SV831: $i] :
( ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SV831 @ SV760 @ SV631 )
| ( ( hAPP @ ( hAPP @ SV631 @ SV447 ) @ ( hAPP @ ( hAPP @ SV631 @ SV447 ) @ SV209 ) )
= ( hAPP @ ( hAPP @ SV631 @ SV447 ) @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6840]) ).
thf(7040,plain,
! [SV212: $i,SV450: $i,SV633: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV633 ) @ SV450 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV633 @ tc_HOL_Obool ) ) @ SV212 ) @ SV450 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV633 ) @ SV212 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6843]) ).
thf(7041,plain,
! [SV213: $i,SV451: $i,SV634: $i,SV761: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV761 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV761 ) @ SV634 ) @ SV451 ) )
| ( SV634 != SV213 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV761 ) @ SV213 ) @ SV451 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6844]) ).
thf(7042,plain,
! [SV214: $i,SV452: $i,SV635: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV635 ) @ SV452 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV452 ) @ SV214 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV635 ) @ SV214 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6845]) ).
thf(7043,plain,
! [SV215: $i,SV453: $i,SV636: $i,SV762: $i] :
( ( ( SV762 != SV636 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV636 ) @ SV215 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV762 ) @ SV215 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6846]) ).
thf(7044,plain,
! [SV216: $i,SV454: $i,SV637: $i,SV763: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV763 ) @ SV637 ) @ SV454 ) @ SV216 ) )
| ( SV637 = SV216 )
| ( hBOOL @ ( hAPP @ SV454 @ SV216 ) ) )
| ~ ( ~ ( ( SV637 = SV216 )
| ( hBOOL @ ( hAPP @ SV454 @ SV216 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV763 ) @ SV637 ) @ SV454 ) @ SV216 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6847]) ).
thf(7045,plain,
! [SV217: $i,SV455: $i,SV638: $i,SV764: $i,SV832: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
| ~ ! [SY2491: $i] :
~ ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SY2491 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2491 ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SY2491 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2491 ) @ SV217 ) ) ) ) )
| ~ ( ~ ~ ! [SY2492: $i] :
~ ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SY2492 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2492 ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SY2492 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2492 ) @ SV217 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6848]) ).
thf(7046,plain,
! [SV218: $i,SV456: $i] :
( ( ( ~ ( class_Finite__Set_Ofinite @ SV456 )
| ~ ( class_Finite__Set_Ofinite @ SV218 ) )
= $true )
| ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV456 @ SV218 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6849]) ).
thf(7047,plain,
! [SV219: $i,SV457: $i,SV639: $i,SV765: $i,SV833: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV833 @ SV765 @ SV639 ) @ SV457 ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV639 @ SV219 ) @ SV457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6850]) ).
thf(7048,plain,
! [SV220: $i,SV458: $i,SV640: $i] :
( ( ( SV640 = SV458 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV220 @ tc_HOL_Obool ) ) @ SV458 ) @ SV640 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6851]) ).
thf(7049,plain,
! [SV221: $i,SV459: $i,SV641: $i,SV766: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequivp @ SV766 @ SV641 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV641 @ SV459 ) @ SV221 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV641 @ SV221 ) @ SV459 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6852]) ).
thf(7050,plain,
! [SV223: $i,SV461: $i,SV642: $i,SV767: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV767 @ SV642 @ SV461 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV767 ) @ tc_HOL_Obool ) ) @ SV223 ) @ SV461 ) )
| ( c_Hoare__Mirabelle_Ohoare__derivs @ SV767 @ SV642 @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6854]) ).
thf(7051,plain,
! [SV224: $i,SV462: $i,SV643: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV643 ) @ SV462 )
!= SV224 )
| ( SV462
= ( hAPP @ ( c_List_Orev @ SV643 ) @ SV224 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6855]) ).
thf(7052,plain,
! [SV224: $i,SV643: $i,SV462: $i] :
( ( ~ ( ( SV462
!= ( hAPP @ ( c_List_Orev @ SV643 ) @ SV224 ) )
| ( ( hAPP @ ( c_List_Orev @ SV643 ) @ SV462 )
= SV224 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6855]) ).
thf(7053,plain,
! [SV225: $i,SV463: $i,SV644: $i,SV768: $i,SV834: $i] :
( ( ~ ( c_Equiv__Relations_Oequivp @ SV834 @ SV768 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV644 ) @ SV463 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV463 ) @ SV225 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV644 ) @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6856]) ).
thf(7054,plain,
! [SV226: $i,SV464: $i,SV645: $i,SV769: $i,SV835: $i] :
( ( ! [SY2493: $i,SY2494: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY2494 @ SY2493 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
| ~ ! [SY2430: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SY2430 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2430 ) @ SV226 ) ) ) )
| ~ ( ~ ~ ! [SY2431: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SY2431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2431 ) @ SV226 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY2494 @ SY2493 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6857]) ).
thf(7055,plain,
! [SV227: $i,SV465: $i,SV646: $i,SV770: $i,SV836: $i] :
( ( ! [SY2497: $i,SY2498: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY2498 @ SY2497 @ SV836 @ SV770 @ SV646 @ SV465 )
| ( ( hAPP @ ( hAPP @ SV836 @ SV227 ) @ SV227 )
= SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6858]) ).
thf(7056,plain,
! [SV228: $i,SV466: $i,SV647: $i,SV771: $i,SV837: $i] :
( ( ! [SY2499: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2499 @ SV837 ) @ SV771 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV647 @ ( tc_fun @ SV466 @ tc_HOL_Obool ) ) ) @ SY2499 ) @ SV228 ) @ SV837 ) @ SV771 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6859]) ).
thf(7057,plain,
! [SV229: $i,SV467: $i,SV648: $i,SV772: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV772 ) @ SV648 ) @ SV467 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV772 @ tc_HOL_Obool ) ) @ SV467 ) @ SV229 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV772 ) @ SV648 ) @ SV229 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6860]) ).
thf(7058,plain,
! [SV230: $i,SV468: $i,SV649: $i,SV773: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV773 ) )
= $true )
| ( ( ( SV649 != SV468 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV773 ) @ SV230 ) @ SV468 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV773 ) @ SV230 ) @ SV649 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6861]) ).
thf(7059,plain,
! [SV231: $i,SV469: $i,SV650: $i] :
( ( ( class_Orderings_Oorder @ SV650 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV650 ) @ SV469 ) @ SV231 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV650 ) @ SV231 ) @ SV469 ) )
| ( SV231 = SV469 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6862]) ).
thf(7060,plain,
! [SV233: $i,SV471: $i,SV651: $i,SV774: $i,SV838: $i] :
( ( ! [SY2500: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2500 @ SV838 ) @ SV774 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV651 @ ( tc_fun @ SV471 @ tc_HOL_Obool ) ) ) @ SV233 ) @ SY2500 ) @ SV838 ) @ SV774 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6864]) ).
thf(7061,plain,
! [SV234: $i,SV472: $i,SV652: $i,SV775: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV775 @ tc_HOL_Obool ) ) @ SV652 ) @ SV472 ) @ SV234 ) ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP @ SV652 @ SV234 ) )
| ( hBOOL @ ( hAPP @ SV472 @ SV234 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6865]) ).
thf(7062,plain,
! [SV235: $i,SV473: $i,SV653: $i,SV776: $i,SV839: $i] :
( ( ! [SY2501: $i,SY2502: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2502 @ SY2501 @ SV839 @ SV776 @ SV653 )
| ~ ( ~ ( ( ( hAPP @ SV839 @ SV473 )
!= ( hAPP @ SV839 @ SV235 ) )
| ( SV473 = SV235 ) )
| ~ ( ( SV473 != SV235 )
| ( ( hAPP @ SV839 @ SV473 )
= ( hAPP @ SV839 @ SV235 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6866]) ).
thf(7063,plain,
! [SV236: $i,SV474: $i,SV654: $i,SV777: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV777 @ tc_HOL_Obool ) ) @ SV654 ) @ SV474 ) @ SV236 ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV654 @ SV236 ) )
| ~ ( hBOOL @ ( hAPP @ SV474 @ SV236 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6867]) ).
thf(7064,plain,
! [SV237: $i,SV475: $i,SV655: $i] :
( ( ( c_Predicate_Oreflp @ SV655 @ SV475 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV475 @ SV237 ) @ SV237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6868]) ).
thf(7065,plain,
! [SV238: $i,SV476: $i,SV656: $i,SV778: $i,SV840: $i] :
( ( ! [SY2503: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2503 @ SV840 @ SV778 @ SV656 @ SV476 )
| ( ( hAPP @ SV656 @ ( hAPP @ SV778 @ SV238 ) )
= SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6869]) ).
thf(7066,plain,
! [SV239: $i,SV477: $i] :
( ( ( ! [SY2052: $i] :
~ ( hBOOL @ ( hAPP @ SV477 @ SY2052 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV477 @ ( c_Hilbert__Choice_OEps @ SV239 @ SV477 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6870]) ).
thf(7067,plain,
! [SV240: $i,SV478: $i,SV657: $i,SV779: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV779 @ tc_HOL_Obool ) ) @ SV657 ) @ SV478 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV779 @ tc_HOL_Obool ) ) @ SV657 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV779 ) @ SV240 ) @ SV478 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6871]) ).
thf(7068,plain,
! [SV241: $i,SV479: $i,SV658: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV658 @ tc_HOL_Obool ) ) @ SV479 ) @ SV241 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV658 @ tc_HOL_Obool ) ) @ SV241 ) @ SV479 ) )
| ( SV479 = SV241 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6872]) ).
thf(7069,plain,
! [SV242: $i,SV480: $i,SV659: $i] :
( ( ( c_Wellfounded_OwfP @ SV659 @ SV480 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV659 @ ( tc_fun @ SV659 @ tc_HOL_Obool ) ) ) @ SV242 ) @ SV480 ) )
| ( c_Wellfounded_OwfP @ SV659 @ SV242 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6873]) ).
thf(7070,plain,
! [SV243: $i,SV481: $i,SV660: $i] :
( ( ( class_Orderings_Oorder @ SV660 )
= $false )
| ( ( ~ ( ~ ( ( SV481 != SV243 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) ) )
| ( SV481 = SV243 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6874]) ).
thf(7071,plain,
! [SV33: $i,SV275: $i,SV501: $i,SV668: $i,SV781: $i,SV841: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV841 @ SV781 @ SV668 @ SV501 ) @ SV275 ) @ SV33 )
= ( hAPP @ SV501 @ ( hAPP @ SV275 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6876]) ).
thf(7072,plain,
! [SV34: $i,SV276: $i,SV502: $i,SV669: $i,SV782: $i,SV842: $i] :
( ( ! [SY2504: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY2504 @ SV842 @ SV782 @ SV669 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV502 @ SY2504 @ SV782 @ SV276 ) @ SV34 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV502 @ SV842 @ SV782 @ ( hAPP @ ( c_Fun_Ocomp @ SY2504 @ SV842 @ SV502 @ SV669 ) @ SV276 ) ) @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6877]) ).
thf(7073,plain,
! [SV35: $i,SV277: $i,SV503: $i,SV670: $i,SV783: $i,SV843: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV843 @ SV783 @ SV670 @ SV503 ) @ SV277 ) @ SV35 )
= ( hAPP @ SV503 @ ( hAPP @ SV277 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6878]) ).
thf(7074,plain,
! [SV40: $i,SV282: $i,SV505: $i,SV672: $i,SV784: $i,SV844: $i] :
( ( ! [SY2505: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2505 @ SV844 @ SV784 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2505 @ SV672 @ SV844 ) @ SV505 ) @ SV282 ) ) @ SV40 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2505 @ SV672 @ SV784 ) @ SV505 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV672 @ SV844 @ SV784 ) @ SV282 ) @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6880]) ).
thf(7075,plain,
! [SV49: $i,SV290: $i,SV511: $i,SV677: $i,SV786: $i,SV845: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SV845 @ SV786 @ SV677 ) @ SV511 ) @ SV290 ) @ SV49 )
= ( hAPP @ SV511 @ ( hAPP @ SV290 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6882]) ).
thf(7076,plain,
! [SV50: $i,SV291: $i,SV512: $i,SV678: $i,SV787: $i,SV846: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SV846 @ SV787 @ SV678 ) @ SV512 ) @ SV291 ) @ SV50 )
= ( hAPP @ ( hAPP @ SV512 @ SV50 ) @ SV291 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6883]) ).
thf(7077,plain,
! [SV51: $i,SV292: $i,SV513: $i,SV679: $i,SV788: $i,SV847: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SV847 @ SV788 @ SV679 ) @ SV513 ) @ SV292 ) @ SV51 )
= ( hAPP @ ( hAPP @ SV513 @ SV51 ) @ ( hAPP @ SV292 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6884]) ).
thf(7078,plain,
! [SV294: $i,SV55: $i] :
( ( ( hBOOL @ SV55 )
= $false )
| ( ( hBOOL @ SV294 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV294 ) @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6885]) ).
thf(7079,plain,
! [SV63: $i,SV302: $i] :
( ( ( hBOOL @ SV302 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV302 ) @ SV63 ) )
= $false )
| ( ( hBOOL @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6887]) ).
thf(7080,plain,
! [SV65: $i,SV304: $i,SV515: $i,SV680: $i] :
( ( ( hBOOL @ ( hAPP @ SV680 @ SV515 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV304 @ SV515 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV65 @ tc_HOL_Obool ) ) @ SV680 ) @ SV304 ) @ SV515 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6889]) ).
thf(7081,plain,
! [SV66: $i,SV305: $i,SV516: $i,SV681: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV681 @ tc_HOL_Obool ) ) @ SV516 ) @ SV305 ) @ SV66 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV516 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6890]) ).
thf(7082,plain,
! [SV67: $i,SV306: $i,SV517: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 )
= SV67 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6891]) ).
thf(7083,plain,
! [SV67: $i,SV306: $i,SV517: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 )
!= SV67 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6892]) ).
thf(7084,plain,
! [SV68: $i,SV307: $i,SV518: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV518 ) @ SV307 ) @ SV68 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV518 ) @ SV68 ) @ SV307 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV518 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6893]) ).
thf(7085,plain,
! [SV69: $i,SV308: $i,SV519: $i,SV682: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV682 @ SV519 @ SV308 ) @ SV69 ) )
| ~ ! [SY1684: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ SY1684 ) @ SV69 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6894]) ).
thf(7086,plain,
! [SV519: $i,SV682: $i,SV69: $i,SV308: $i] :
( ( ~ ( ~ ~ ! [SY1685: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ SY1685 ) @ SV69 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV682 @ SV519 @ SV308 ) @ SV69 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6894]) ).
thf(7087,plain,
! [SV70: $i,SV309: $i] :
( ( ( ~ ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY1062: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1062 ) @ SY1062 ) )
| ~ ! [SY1063: $i,SY1064: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1064 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1064 ) @ SY1064 ) ) )
| ( ( hAPP @ SV70 @ SY1063 )
!= ( hAPP @ SV70 @ SY1064 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1064 ) @ SY1064 ) ) )
| ( ( hAPP @ SV70 @ SY1063 )
!= ( hAPP @ SV70 @ SY1064 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1064 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6895]) ).
thf(7088,plain,
! [SV309: $i,SV70: $i] :
( ( ( ~ ~ ( ~ ~ ! [SY1065: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1065 ) @ SY1065 ) )
| ~ ! [SY1066: $i,SY1067: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6896]) ).
thf(7089,plain,
! [SV71: $i,SV310: $i,SV520: $i,SV683: $i] :
( ( ( SV683 = SV520 )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV683 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV520 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV520 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV683 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6897]) ).
thf(7090,plain,
! [SV73: $i,SV312: $i,SV521: $i,SV684: $i,SV789: $i,SV848: $i] :
( ( ! [SY2506: $i,SY2507: $i,SY2508: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2508 @ SY2507 @ SY2506 @ SV848 ) @ SV789 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV684 @ SY2507 @ SY2506 @ SV521 ) @ SV312 ) )
| ( ( hAPP @ SV848 @ ( hAPP @ SV789 @ SV73 ) )
= ( hAPP @ SV521 @ ( hAPP @ SV312 @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6898]) ).
thf(7091,plain,
! [SV74: $i,SV313: $i,SV522: $i,SV685: $i] :
( ( ( class_Orderings_Oord @ SV685 )
= $false )
| ( ( ~ ! [SY2341: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV685 ) @ ( hAPP @ SV522 @ SY2341 ) ) @ ( hAPP @ SV313 @ SY2341 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV74 @ SV685 ) ) @ SV522 ) @ SV313 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6899]) ).
thf(7092,plain,
! [SV75: $i,SV314: $i,SV523: $i,SV686: $i,SV790: $i,SV849: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV849 @ SV790 ) @ SV686 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV523 @ SV790 ) @ SV686 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV314 @ ( tc_fun @ SV75 @ tc_HOL_Obool ) ) ) @ SV849 ) @ SV523 ) @ SV790 ) @ SV686 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6900]) ).
thf(7093,plain,
! [SV315: $i,SV524: $i,SV77: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV77 @ tc_HOL_Obool ) ) @ SV524 ) @ SV315 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV77 @ tc_HOL_Obool ) ) @ SV315 ) @ SV524 ) ) )
= $false )
| ( ( SV524 = SV315 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6901]) ).
thf(7094,plain,
! [SV82: $i,SV320: $i,SV527: $i,SV687: $i] :
( ( ( c_Finite__Set_Ofolding__one__idem @ SV687 @ SV527 @ SV320 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV527 @ SV82 ) @ SV82 )
= SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6904]) ).
thf(7095,plain,
! [SV84: $i,SV322: $i,SV528: $i,SV688: $i,SV791: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV791 @ tc_HOL_Obool ) ) @ SV688 ) @ SV528 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV322 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV322 @ SV791 @ SV84 ) @ SV688 ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV322 @ SV791 @ SV84 ) @ SV528 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6905]) ).
thf(7096,plain,
! [SV85: $i,SV323: $i,SV529: $i] :
( ( ( ! [SY2115: $i] :
~ ( hBOOL @ ( hAPP @ SV529 @ SY2115 ) ) )
= $true )
| ( ( ( SV323
!= ( c_Hilbert__Choice_OEps @ SV85 @ SV529 ) )
| ( hBOOL @ ( hAPP @ SV529 @ SV323 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6906]) ).
thf(7097,plain,
! [SV86: $i,SV324: $i,SV530: $i,SV689: $i] :
( ( ( SV689 = SV530 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6907]) ).
thf(7098,plain,
! [SV87: $i,SV325: $i,SV531: $i,SV690: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV690 @ tc_HOL_Obool ) ) @ SV531 ) @ SV325 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV690 @ tc_HOL_Obool ) ) @ SV325 ) @ SV87 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV690 @ tc_HOL_Obool ) ) @ SV531 ) @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6908]) ).
thf(7099,plain,
! [SV88: $i,SV326: $i,SV532: $i,SV691: $i,SV792: $i,SV850: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV850 @ ( tc_fun @ SV792 @ tc_HOL_Obool ) ) ) @ SV691 ) @ SV532 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV691 @ SV326 ) @ SV88 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV532 @ SV326 ) @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6909]) ).
thf(7100,plain,
! [SV89: $i,SV327: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ SV327 )
!= ( hAPP @ c_Int_ORep__Integ @ SV89 ) )
= $true )
| ( ( SV327 = SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6910]) ).
thf(7101,plain,
! [SV89: $i,SV327: $i] :
( ( ( SV327 != SV89 )
= $true )
| ( ( ( hAPP @ c_Int_ORep__Integ @ SV327 )
= ( hAPP @ c_Int_ORep__Integ @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6911]) ).
thf(7102,plain,
! [SV90: $i,SV328: $i,SV533: $i,SV692: $i,SV793: $i,SV851: $i] :
( ( ~ ( ( SV851 != SV793 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV692 @ SV533 @ SV328 @ SV793 @ SV90 ) @ SV851 )
= ( hAPP @ SV328 @ SV851 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6912]) ).
thf(7103,plain,
! [SV91: $i,SV329: $i,SV534: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV534 ) @ SV329 )
!= ( hAPP @ ( c_List_Orev @ SV534 ) @ SV91 ) )
| ( SV329 = SV91 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6913]) ).
thf(7104,plain,
! [SV534: $i,SV91: $i,SV329: $i] :
( ( ( SV329 != SV91 )
| ( ( hAPP @ ( c_List_Orev @ SV534 ) @ SV329 )
= ( hAPP @ ( c_List_Orev @ SV534 ) @ SV91 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6914]) ).
thf(7105,plain,
! [SV92: $i,SV330: $i,SV535: $i,SV693: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV693 @ SV535 @ SV330 ) @ SV92 ) )
| ~ ! [SY1733: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ SY1733 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6915]) ).
thf(7106,plain,
! [SV535: $i,SV693: $i,SV92: $i,SV330: $i] :
( ( ~ ( ~ ~ ! [SY1734: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ SY1734 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV693 @ SV535 @ SV330 ) @ SV92 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6915]) ).
thf(7107,plain,
! [SV95: $i,SV333: $i,SV537: $i,SV694: $i,SV794: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ SV694 ) @ SV537 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ SV333 ) @ SV95 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ SV694 ) @ SV333 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ SV537 ) @ SV95 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6917]) ).
thf(7108,plain,
! [SV96: $i,SV334: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV334 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV96 ) )
= $true )
| ( ( SV334 = SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6918]) ).
thf(7109,plain,
! [SV96: $i,SV334: $i] :
( ( ( SV334 != SV96 )
= $true )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV334 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6919]) ).
thf(7110,plain,
! [SV97: $i,SV335: $i,SV538: $i,SV695: $i,SV795: $i,SV852: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV852 @ ( tc_fun @ SV795 @ tc_HOL_Obool ) ) ) @ SV695 ) @ SV538 ) @ SV335 ) @ SV97 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV695 @ SV335 ) @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6920]) ).
thf(7111,plain,
! [SV99: $i,SV337: $i,SV540: $i,SV696: $i,SV796: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV796 @ SV696 @ SV540 ) @ SV337 ) @ SV99 ) )
| ( hBOOL @ ( hAPP @ SV337 @ ( hAPP @ SV540 @ SV99 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV337 @ ( hAPP @ SV540 @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV796 @ SV696 @ SV540 ) @ SV337 ) @ SV99 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6922]) ).
thf(7112,plain,
! [SV100: $i,SV338: $i,SV541: $i,SV697: $i,SV797: $i,SV853: $i] :
( ( ! [SY2509: $i,SY2510: $i,SY2511: $i,SY2512: $i,SY2513: $i] :
( ( ( hAPP @ SY2513 @ ( hAPP @ SY2512 @ SY2511 ) )
!= ( hAPP @ SY2510 @ ( hAPP @ SY2509 @ SV853 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV797 @ SV697 @ SV541 @ SY2513 ) @ SY2512 ) @ SY2511 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV338 @ SV697 @ SV100 @ SY2510 ) @ SY2509 ) @ SV853 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6923]) ).
thf(7113,plain,
! [SV101: $i,SV339: $i,SV542: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV339 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) @ SV339 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6924]) ).
thf(7114,plain,
! [SV339: $i,SV101: $i,SV542: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) @ SV339 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV339 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6925]) ).
thf(7115,plain,
! [SV102: $i,SV340: $i,SV543: $i,SV698: $i,SV798: $i,SV854: $i] :
( ( ~ ( c_Finite__Set_Ofun__left__comm @ SV854 @ SV798 @ SV698 )
| ( ( hAPP @ ( hAPP @ SV698 @ SV543 ) @ ( hAPP @ ( hAPP @ SV698 @ SV340 ) @ SV102 ) )
= ( hAPP @ ( hAPP @ SV698 @ SV340 ) @ ( hAPP @ ( hAPP @ SV698 @ SV543 ) @ SV102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6926]) ).
thf(7116,plain,
! [SV103: $i,SV341: $i,SV544: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV103 ) )
| ! [SY2145: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SY2145 ) @ SV103 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SY2145 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6927]) ).
thf(7117,plain,
! [SV544: $i,SV103: $i,SV341: $i] :
( ( ~ ! [SY2146: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SY2146 ) @ SV103 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SY2146 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV103 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6928]) ).
thf(7118,plain,
! [SV105: $i,SV343: $i,SV546: $i,SV699: $i,SV799: $i] :
( ( ( ~ ( c_Equiv__Relations_Opart__equivp @ SV799 @ SV699 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV546 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV343 ) @ SV105 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV546 ) @ SV105 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6930]) ).
thf(7119,plain,
! [SV108: $i,SV855: $i,SV346: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV346 @ SV855 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV346 @ ( c_Hilbert__Choice_OEps @ SV108 @ SV346 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6931]) ).
thf(7120,plain,
! [SV109: $i,SV347: $i,SV547: $i,SV700: $i,SV800: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV800 @ SV700 ) @ SV547 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV347 @ SV109 @ SV800 ) @ SV547 ) @ SV700 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6932]) ).
thf(7121,plain,
! [SV110: $i,SV348: $i,SV548: $i,SV701: $i,SV801: $i] :
( ( ~ ( ( ( c_Fun_Ofun__upd @ SV801 @ SV701 @ SV548 @ SV348 @ SV110 )
!= SV548 )
| ( ( hAPP @ SV548 @ SV348 )
= SV110 ) )
| ~ ( ( ( hAPP @ SV548 @ SV348 )
!= SV110 )
| ( ( c_Fun_Ofun__upd @ SV801 @ SV701 @ SV548 @ SV348 @ SV110 )
= SV548 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6933]) ).
thf(7122,plain,
! [SV112: $i,SV350: $i,SV550: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV112 ) )
| ! [SY2153: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV350 @ SY2153 ) @ SV112 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SY2153 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6935]) ).
thf(7123,plain,
! [SV550: $i,SV112: $i,SV350: $i] :
( ( ~ ! [SY2154: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV350 @ SY2154 ) @ SV112 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SY2154 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV112 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6936]) ).
thf(7124,plain,
! [SV113: $i,SV351: $i,SV551: $i,SV702: $i] :
( ( ( c_Predicate_Osymp @ SV702 @ SV551 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV551 @ SV351 ) @ SV113 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV551 @ SV113 ) @ SV351 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6937]) ).
thf(7125,plain,
! [SV114: $i,SV352: $i,SV552: $i,SV703: $i,SV802: $i,SV856: $i] :
( ( ~ ( ~ ( ( SV856 != SV802 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV703 @ SV552 @ SV352 @ SV802 @ SV114 ) @ SV856 )
= SV114 ) )
| ~ ( ~ ( ( SV856 != SV802 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV703 @ SV552 @ SV352 @ SV802 @ SV114 ) @ SV856 )
= ( hAPP @ SV352 @ SV856 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6938]) ).
thf(7126,plain,
! [SV353: $i,SV115: $i,SV553: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV553 ) @ SV115 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV553 ) @ SV353 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV553 @ tc_HOL_Obool ) ) @ SV353 ) @ SV115 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6939]) ).
thf(7127,plain,
! [SV116: $i,SV354: $i] :
( ( ( ~ ( class_Enum_Oenum @ SV354 ) )
= $true )
| ( ( ~ ( class_Enum_Oenum @ SV116 ) )
= $true )
| ( ( class_Enum_Oenum @ ( tc_fun @ SV354 @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6940]) ).
thf(7128,plain,
! [SV117: $i,SV355: $i,SV554: $i,SV704: $i,SV803: $i,SV857: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV704 ) @ SV554 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV355 ) @ SV117 ) )
| ~ ( ( SV704 != SV355 )
| ( SV554 != SV117 ) ) )
| ~ ( ~ ~ ( ( SV704 != SV355 )
| ( SV554 != SV117 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV704 ) @ SV554 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV355 ) @ SV117 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6941]) ).
thf(7129,plain,
! [SV356: $i,SV118: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV118 ) @ SV356 ) )
= $false )
| ( ( SV356 = SV118 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV356 ) @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6942]) ).
thf(7130,plain,
! [SV119: $i,SV357: $i,SV555: $i,SV705: $i,SV804: $i,SV858: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV858 @ ( tc_fun @ SV804 @ tc_HOL_Obool ) ) ) @ SV705 ) @ SV555 ) @ SV357 ) @ SV119 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV555 @ SV357 ) @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6943]) ).
thf(7131,plain,
! [SV120: $i,SV358: $i,SV556: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
| ( SV358 = SV120 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6944]) ).
thf(7132,plain,
! [SV120: $i,SV358: $i,SV556: $i] :
( ( ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
| ( SV358 = SV120 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6945]) ).
thf(7133,plain,
! [SV121: $i,SV359: $i,SV557: $i,SV706: $i] :
( ( ( class_Orderings_Oord @ SV706 )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV557 @ SV706 ) ) @ SV359 ) @ SV121 ) )
| ! [SY2373: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV706 ) @ ( hAPP @ SV359 @ SY2373 ) ) @ ( hAPP @ SV121 @ SY2373 ) ) ) )
| ~ ( ~ ! [SY2374: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV706 ) @ ( hAPP @ SV359 @ SY2374 ) ) @ ( hAPP @ SV121 @ SY2374 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV557 @ SV706 ) ) @ SV359 ) @ SV121 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6946]) ).
thf(7134,plain,
! [SV123: $i,SV361: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV361 @ ( c_Hilbert__Choice_OEps @ SV123 @ SV361 ) ) ) )
= $true )
| ( ( ~ ! [SY1800: $i] :
~ ( hBOOL @ ( hAPP @ SV361 @ SY1800 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6948]) ).
thf(7135,plain,
! [SV123: $i,SV361: $i] :
( ( ( ~ ~ ! [SY1801: $i] :
~ ( hBOOL @ ( hAPP @ SV361 @ SY1801 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV361 @ ( c_Hilbert__Choice_OEps @ SV123 @ SV361 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6949]) ).
thf(7136,plain,
! [SV125: $i,SV363: $i,SV559: $i,SV707: $i,SV805: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV805 @ SV707 @ SV559 @ SV363 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV805 @ tc_HOL_Obool ) ) @ SV125 ) @ SV363 ) )
| ( c_Fun_Oinj__on @ SV805 @ SV707 @ SV559 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6951]) ).
thf(7137,plain,
! [SV126: $i,SV364: $i,SV560: $i,SV708: $i] :
( ( ( class_Orderings_Oord @ SV708 )
= $false )
| ( ( ( SV560 != SV364 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV708 ) @ SV364 ) @ SV126 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV708 ) @ SV560 ) @ SV126 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6952]) ).
thf(7138,plain,
! [SV127: $i,SV365: $i,SV561: $i,SV709: $i,SV806: $i,SV859: $i] :
( ( ! [SY2514: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2514 @ SV859 @ SV806 @ SV709 ) @ SV561 )
!= SV365 )
| ( ( hAPP @ SV709 @ ( hAPP @ SV561 @ SV127 ) )
= ( hAPP @ SV365 @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6953]) ).
thf(7139,plain,
! [SV128: $i,SV366: $i,SV562: $i,SV710: $i,SV807: $i,SV860: $i] :
( ( ~ ( ~ ( ( SV860 != SV807 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV710 @ SV562 @ SV366 @ SV807 @ SV128 ) @ SV860 )
= SV128 ) )
| ~ ( ~ ( ( SV860 != SV807 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV710 @ SV562 @ SV366 @ SV807 @ SV128 ) @ SV860 )
= ( hAPP @ SV366 @ SV860 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6954]) ).
thf(7140,plain,
! [SV129: $i,SV367: $i,SV563: $i,SV711: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV367 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV129 ) )
| ( SV367 = SV129 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6955]) ).
thf(7141,plain,
! [SV563: $i,SV711: $i,SV129: $i,SV367: $i] :
( ( ~ ( ( SV367 != SV129 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV367 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV129 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6955]) ).
thf(7142,plain,
! [SV130: $i,SV368: $i,SV564: $i,SV712: $i] :
( ( ( class_Orderings_Opreorder @ SV712 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV712 ) @ SV564 ) @ SV368 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV712 ) @ SV368 ) @ SV130 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV712 ) @ SV564 ) @ SV130 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6956]) ).
thf(7143,plain,
! [SV131: $i,SV369: $i,SV565: $i,SV713: $i] :
( ( ( SV713 = SV565 )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV713 ) @ SV131 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV565 ) @ SV131 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV565 ) @ SV131 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV713 ) @ SV131 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6957]) ).
thf(7144,plain,
! [SV132: $i,SV370: $i,SV566: $i,SV714: $i,SV808: $i,SV861: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV861 ) @ SV808 ) @ SV714 )
!= SV566 )
| ( SV370
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV861 ) @ SV714 ) @ SV132 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV861 ) @ SV808 ) @ SV370 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV861 ) @ SV566 ) @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6958]) ).
thf(7145,plain,
! [SV133: $i,SV371: $i,SV567: $i,SV715: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV567 ) @ SV371 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV133 ) @ SV371 ) )
| ( SV567 = SV133 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6959]) ).
thf(7146,plain,
! [SV371: $i,SV715: $i,SV133: $i,SV567: $i] :
( ( ~ ( ( SV567 != SV133 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV567 ) @ SV371 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV133 ) @ SV371 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6959]) ).
thf(7147,plain,
! [SV134: $i,SV372: $i,SV568: $i,SV716: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV716 @ tc_HOL_Obool ) ) @ SV568 ) @ SV372 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV568 @ SV134 ) )
| ( hBOOL @ ( hAPP @ SV372 @ SV134 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6960]) ).
thf(7148,plain,
! [SV135: $i,SV373: $i,SV569: $i,SV717: $i] :
( ( ( c_Equiv__Relations_Opart__equivp @ SV717 @ SV569 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV569 @ SV373 ) @ SV135 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV569 @ SV135 ) @ SV373 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6961]) ).
thf(7149,plain,
! [SV136: $i,SV374: $i,SV570: $i,SV718: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV718 @ SV570 ) @ SV374 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV718 @ SV570 ) @ SV136 ) )
| ( SV374 = SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6962]) ).
thf(7150,plain,
! [SV137: $i,SV375: $i,SV571: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV571 ) @ SV375 ) @ SV137 ) )
| ( hBOOL @ ( hAPP @ SV137 @ SV375 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6963]) ).
thf(7151,plain,
! [SV571: $i,SV375: $i,SV137: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV137 @ SV375 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV571 ) @ SV375 ) @ SV137 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6964]) ).
thf(7152,plain,
! [SV140: $i,SV378: $i,SV574: $i,SV719: $i,SV809: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV809 @ SV719 ) @ SV574 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV378 @ SV140 @ SV809 ) @ SV574 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6967]) ).
thf(7153,plain,
! [SV141: $i,SV379: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV379 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV141 ) )
= $true )
| ( ( SV379 = SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6968]) ).
thf(7154,plain,
! [SV141: $i,SV379: $i] :
( ( ( SV379 != SV141 )
= $true )
| ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV379 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6969]) ).
thf(7155,plain,
! [SV142: $i,SV380: $i,SV575: $i,SV720: $i,SV810: $i,SV862: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV862 @ ( tc_fun @ SV810 @ tc_HOL_Obool ) ) ) @ SV720 ) @ SV575 ) @ SV380 ) @ SV142 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV720 @ SV380 ) @ SV142 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV575 @ SV380 ) @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6970]) ).
thf(7156,plain,
! [SV143: $i,SV381: $i,SV576: $i,SV721: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV576 ) @ SV381 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV576 ) @ SV143 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV576 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV381 ) @ SV143 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6971]) ).
thf(7157,plain,
! [SV144: $i,SV382: $i,SV577: $i] :
( ( ( SV577 != SV382 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV577 ) @ SV382 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV382 ) @ SV577 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6972]) ).
thf(7158,plain,
! [SV382: $i,SV577: $i,SV144: $i] :
( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV577 ) @ SV382 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV382 ) @ SV577 ) ) )
| ( SV577 = SV382 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6973]) ).
thf(7159,plain,
! [SV146: $i,SV384: $i,SV579: $i,SV722: $i] :
( ( ( hBOOL @ ( hAPP @ SV722 @ SV579 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV384 @ tc_HOL_Obool ) ) @ SV722 ) @ SV146 ) )
| ( hBOOL @ ( hAPP @ SV146 @ SV579 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6975]) ).
thf(7160,plain,
! [SV147: $i,SV385: $i,SV580: $i,SV723: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV723 @ tc_HOL_Obool ) ) @ SV580 ) @ SV385 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV723 @ tc_HOL_Obool ) ) @ SV385 ) @ SV147 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV723 @ tc_HOL_Obool ) ) @ SV580 ) @ SV147 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6976]) ).
thf(7161,plain,
! [SV581: $i,SV148: $i,SV386: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV386 ) @ SV148 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV581 ) @ SV148 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV581 ) @ SV386 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6977]) ).
thf(7162,plain,
! [SV149: $i,SV387: $i,SV582: $i,SV724: $i] :
( ( ( hBOOL @ ( hAPP @ SV724 @ SV582 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV387 @ tc_HOL_Obool ) ) @ SV724 ) @ SV149 ) @ SV582 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6978]) ).
thf(7163,plain,
! [SV150: $i,SV388: $i,SV583: $i,SV725: $i,SV811: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV811 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV725 @ SV811 ) ) @ SV583 ) @ SV388 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV811 ) @ ( hAPP @ SV583 @ SV150 ) ) @ ( hAPP @ SV388 @ SV150 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6979]) ).
thf(7164,plain,
! [SV151: $i,SV389: $i,SV584: $i,SV726: $i,SV812: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV812 @ SV726 ) @ SV584 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV389 @ SV151 @ SV812 ) @ SV726 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6980]) ).
thf(7165,plain,
! [SV152: $i,SV390: $i,SV585: $i,SV727: $i,SV813: $i,SV863: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV863 @ SV813 ) @ SV727 ) @ SV585 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV863 @ SV813 ) @ SV390 ) @ SV152 ) )
| ~ ( ( SV727 != SV390 )
| ( SV585 != SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6981]) ).
thf(7166,plain,
! [SV153: $i,SV391: $i,SV586: $i,SV728: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV728 @ tc_HOL_Obool ) ) @ SV586 ) @ SV391 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV728 ) @ SV153 ) @ SV586 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV728 ) @ SV153 ) @ SV391 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6982]) ).
thf(7167,plain,
! [SV154: $i,SV392: $i,SV587: $i,SV729: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV729 @ tc_HOL_Obool ) ) @ SV587 ) @ SV392 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV729 ) @ SV154 ) @ SV587 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV729 ) @ SV154 ) @ SV392 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6983]) ).
thf(7168,plain,
! [SV155: $i,SV393: $i,SV588: $i,SV730: $i,SV814: $i,SV864: $i] :
( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV864 @ SV814 ) @ SV730 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV588 @ SV814 ) @ SV730 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV393 @ ( tc_fun @ SV155 @ tc_HOL_Obool ) ) ) @ SV588 ) @ SV864 ) @ SV814 ) @ SV730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6984]) ).
thf(7169,plain,
! [SV156: $i,SV394: $i,SV589: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
| ~ ( ( SV394 != SV156 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6985]) ).
thf(7170,plain,
! [SV156: $i,SV394: $i,SV589: $i] :
( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
| ~ ( ( SV394 != SV156 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6986]) ).
thf(7171,plain,
! [SV157: $i,SV395: $i,SV590: $i,SV731: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV731 @ tc_HOL_Obool ) ) @ SV590 ) @ SV395 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV731 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV731 ) @ SV157 ) @ SV590 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV731 ) @ SV157 ) @ SV395 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6987]) ).
thf(7172,plain,
! [SV159: $i,SV397: $i,SV591: $i,SV732: $i,SV815: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV815 @ SV732 @ SV591 ) @ SV397 ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV591 @ SV159 ) @ SV397 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV591 @ SV159 ) @ SV397 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV815 @ SV732 @ SV591 ) @ SV397 ) @ SV159 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6988]) ).
thf(7173,plain,
! [SV160: $i,SV398: $i,SV592: $i,SV733: $i,SV816: $i] :
( ( ( ~ ( c_Predicate_Otransp @ SV816 @ SV733 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV592 ) @ SV398 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV398 ) @ SV160 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV592 ) @ SV160 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6989]) ).
thf(7174,plain,
! [SV161: $i,SV399: $i,SV593: $i] :
( ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV399 )
!= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV161 ) )
| ( SV399 = SV161 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6990]) ).
thf(7175,plain,
! [SV593: $i,SV161: $i,SV399: $i] :
( ( ( SV399 != SV161 )
| ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV399 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV161 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6991]) ).
thf(7176,plain,
! [SV162: $i,SV400: $i,SV594: $i,SV734: $i,SV817: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV817 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV734 @ SV817 ) ) @ SV594 ) @ SV400 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV817 ) @ ( hAPP @ SV594 @ SV162 ) ) @ ( hAPP @ SV400 @ SV162 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6992]) ).
thf(7177,plain,
! [SV163: $i,SV401: $i,SV595: $i,SV735: $i] :
( ( ( class_Orderings_Oorder @ SV735 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV735 ) @ SV595 ) @ SV401 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV735 ) @ SV163 ) @ SV595 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV735 ) @ SV163 ) @ SV401 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6993]) ).
thf(7178,plain,
! [SV164: $i,SV402: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV402 )
!= ( hAPP @ c_Nat_OSuc @ SV164 ) )
= $true )
| ( ( SV402 = SV164 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6994]) ).
thf(7179,plain,
! [SV164: $i,SV402: $i] :
( ( ( SV402 != SV164 )
= $true )
| ( ( ( hAPP @ c_Nat_OSuc @ SV402 )
= ( hAPP @ c_Nat_OSuc @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6995]) ).
thf(7180,plain,
! [SV165: $i,SV403: $i,SV596: $i,SV736: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV736 @ SV596 ) @ SV403 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV596 @ SV165 ) @ SV403 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV736 @ SV596 ) @ SV165 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6996]) ).
thf(7181,plain,
! [SV166: $i,SV404: $i,SV597: $i,SV737: $i] :
( ( ( class_Orderings_Oord @ SV737 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV737 ) @ SV597 ) @ SV404 ) )
| ( SV404 != SV166 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV737 ) @ SV597 ) @ SV166 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6997]) ).
thf(7182,plain,
! [SV167: $i,SV405: $i,SV598: $i,SV738: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV738 @ tc_HOL_Obool ) ) @ SV598 ) @ SV405 ) @ SV167 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV405 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6998]) ).
thf(7183,plain,
! [SV169: $i,SV407: $i,SV600: $i,SV739: $i,SV818: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
| ~ ! [SY2478: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SY2478 ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SY2478 ) ) ) )
| ~ ( ~ ~ ! [SY2479: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SY2479 ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SY2479 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7000]) ).
thf(7184,plain,
! [SV170: $i,SV408: $i,SV601: $i,SV740: $i,SV819: $i,SV865: $i] :
( ( ( SV865 != SV819 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV740 @ SV601 @ SV408 ) @ SV170 ) @ SV865 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV740 @ SV601 @ SV408 ) @ SV170 ) @ SV819 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7001]) ).
thf(7185,plain,
! [SV171: $i,SV409: $i,SV602: $i,SV741: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV741 @ SV602 ) )
| ( hBOOL @ ( hAPP @ SV409 @ SV602 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV171 @ tc_HOL_Obool ) ) @ SV409 ) @ SV741 ) @ SV602 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7002]) ).
thf(7186,plain,
! [SV172: $i,SV410: $i,SV603: $i,SV742: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV742 @ tc_HOL_Obool ) ) @ SV603 ) @ SV410 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV742 @ tc_HOL_Obool ) ) @ SV410 ) @ SV172 ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV742 @ tc_HOL_Obool ) ) @ SV410 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV742 @ tc_HOL_Obool ) ) @ SV172 ) @ SV603 ) )
= SV603 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7003]) ).
thf(7187,plain,
! [SV173: $i,SV411: $i,SV604: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV604 ) @ SV411 ) @ SV173 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV604 ) @ SV173 ) @ SV411 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV604 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7004]) ).
thf(7188,plain,
! [SV174: $i,SV412: $i,SV605: $i,SV743: $i] :
( ( ( hBOOL @ ( hAPP @ SV743 @ SV605 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV412 @ tc_HOL_Obool ) ) @ SV174 ) @ SV743 ) @ SV605 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7005]) ).
thf(7189,plain,
! [SV177: $i,SV415: $i,SV606: $i,SV744: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV744 @ tc_HOL_Obool ) ) @ SV606 ) @ SV415 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV744 ) @ SV177 ) @ SV606 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV744 ) @ SV177 ) @ SV415 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7006]) ).
thf(7190,plain,
! [SV178: $i,SV416: $i,SV607: $i,SV745: $i,SV820: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV745 ) @ SV607 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV416 ) @ SV178 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV745 ) @ SV416 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV607 ) @ SV178 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7007]) ).
thf(7191,plain,
! [SV179: $i,SV417: $i,SV608: $i,SV746: $i,SV821: $i,SV866: $i] :
( ( ~ ( ( SV866 != SV821 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ SV608 ) @ SV866 ) @ SV417 ) ) @ SV821 ) @ SV179 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ SV608 ) @ SV821 ) @ SV179 ) ) @ SV866 ) @ SV417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7008]) ).
thf(7192,plain,
! [SV180: $i,SV418: $i,SV609: $i,SV747: $i,SV822: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV747 ) @ SV609 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV418 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ SV822 @ SV418 @ SV180 ) @ SV747 ) ) @ ( hAPP @ ( c_Set_Oimage @ SV822 @ SV418 @ SV180 ) @ SV609 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7009]) ).
thf(7193,plain,
! [SV181: $i,SV419: $i,SV610: $i,SV748: $i,SV823: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV823 @ SV748 @ SV610 ) @ SV419 ) @ SV181 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV610 @ SV181 ) @ SV419 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV610 @ SV181 ) @ SV419 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV823 @ SV748 @ SV610 ) @ SV419 ) @ SV181 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7010]) ).
thf(7194,plain,
! [SV182: $i,SV420: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV420 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV182 ) )
= $true )
| ( ( SV420 = SV182 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7011]) ).
thf(7195,plain,
! [SV182: $i,SV420: $i] :
( ( ( SV420 != SV182 )
= $true )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV420 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7012]) ).
thf(7196,plain,
! [SV183: $i,SV421: $i,SV611: $i,SV749: $i,SV824: $i,SV867: $i] :
( ( ! [SY2515: $i,SY2516: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2516 @ SY2515 @ SV867 @ SV824 ) @ SV749 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV611 @ SY2515 @ SV867 @ SV421 ) @ SV183 ) )
| ! [SY2485: $i] :
( ( hAPP @ SV824 @ ( hAPP @ SV749 @ SY2485 ) )
= ( hAPP @ SV421 @ ( hAPP @ SV183 @ SY2485 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7013]) ).
thf(7197,plain,
! [SV184: $i,SV422: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 ) )
= $true )
| ( ( ! [SY1423: $i,SY1424: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1423 ) @ SY1424 ) )
| ( ( hAPP @ SV184 @ SY1423 )
= ( hAPP @ SV184 @ SY1424 ) ) )
| ~ ( ( ( hAPP @ SV184 @ SY1423 )
!= ( hAPP @ SV184 @ SY1424 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1423 ) @ SY1424 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7014]) ).
thf(7198,plain,
! [SV422: $i,SV184: $i] :
( ( ( ~ ! [SY1425: $i,SY1426: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1425 ) @ SY1426 ) )
| ( ( hAPP @ SV184 @ SY1425 )
= ( hAPP @ SV184 @ SY1426 ) ) )
| ~ ( ( ( hAPP @ SV184 @ SY1425 )
!= ( hAPP @ SV184 @ SY1426 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1425 ) @ SY1426 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7015]) ).
thf(7199,plain,
! [SV185: $i,SV423: $i,SV612: $i,SV750: $i,SV825: $i] :
( ( ( ( hAPP @ SV825 @ SV750 )
!= SV612 )
= $true )
| ( ( ( c_Fun_Ofun__upd @ SV423 @ SV185 @ SV825 @ SV750 @ SV612 )
= SV825 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7016]) ).
thf(7200,plain,
! [SV186: $i,SV424: $i,SV613: $i,SV751: $i,SV826: $i,SV868: $i] :
( ( ! [SY2518: $i,SY2519: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2519 @ SY2518 ) @ SV868 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV826 @ SV868 ) @ SV751 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV613 @ SV424 @ SV186 @ SY2519 @ SV826 ) @ SY2518 ) @ SV751 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7017]) ).
thf(7201,plain,
! [SV187: $i,SV425: $i,SV614: $i,SV752: $i,SV827: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV752 ) @ SV614 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV425 ) @ SV187 ) )
| ~ ( ( SV752 != SV425 )
| ( SV614 != SV187 ) ) )
| ~ ( ~ ~ ( ( SV752 != SV425 )
| ( SV614 != SV187 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV752 ) @ SV614 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV425 ) @ SV187 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7018]) ).
thf(7202,plain,
! [SV427: $i,SV189: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV189 ) @ SV427 ) )
= $false )
| ( ( SV427 = SV189 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV427 ) @ SV189 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7019]) ).
thf(7203,plain,
! [SV191: $i,SV429: $i,SV616: $i,SV753: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SV616 ) @ SV429 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SV429 ) @ SV191 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SV616 ) @ SV191 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7021]) ).
thf(7204,plain,
! [SV192: $i,SV430: $i,SV617: $i,SV754: $i,SV828: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ SV754 ) @ SV617 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ SV430 ) @ SV192 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ SV754 ) @ SV192 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ SV617 ) @ SV430 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7022]) ).
thf(7205,plain,
! [SV196: $i,SV434: $i,SV620: $i,SV755: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV755 @ tc_HOL_Obool ) ) @ SV620 ) @ SV434 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV755 @ tc_HOL_Obool ) ) @ SV434 ) @ SV196 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV755 @ tc_HOL_Obool ) ) @ SV620 ) @ SV196 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7024]) ).
thf(7206,plain,
! [SV197: $i,SV435: $i,SV621: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV621 @ SV435 ) @ SV197 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV435 @ SV197 ) @ SV197 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7025]) ).
thf(7207,plain,
! [SV621: $i,SV197: $i,SV435: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV435 @ SV197 ) @ SV197 ) )
| ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV621 @ SV435 ) @ SV197 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7026]) ).
thf(7208,plain,
! [SV198: $i,SV436: $i,SV622: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV622 ) @ SV436 ) @ SV198 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV622 ) @ SV198 ) @ SV436 ) )
| ( SV436 = SV198 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV622 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7027]) ).
thf(7209,plain,
! [SV199: $i,SV437: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) @ SV199 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) ) ) )
= $true )
| ( ( SV199
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7028]) ).
thf(7210,plain,
! [SV437: $i,SV199: $i] :
( ( ( SV199
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) @ SV199 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7029]) ).
thf(7211,plain,
! [SV200: $i,SV438: $i,SV623: $i,SV756: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV756 @ tc_HOL_Obool ) ) @ SV623 ) @ SV438 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV756 @ tc_HOL_Obool ) ) @ SV200 ) @ SV438 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV756 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV756 @ tc_HOL_Obool ) ) @ SV623 ) @ SV200 ) ) @ SV438 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7030]) ).
thf(7212,plain,
! [SV201: $i,SV439: $i,SV624: $i,SV757: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV757 @ SV624 @ SV439 )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV757 @ SV201 @ SV624 )
| ( c_Hoare__Mirabelle_Ohoare__derivs @ SV757 @ SV201 @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7031]) ).
thf(7213,plain,
! [SV202: $i,SV440: $i,SV625: $i] :
( ( ~ ! [SY2261: $i] : ( hBOOL @ ( hAPP @ SV625 @ SY2261 ) )
| ! [SY2262: $i,SY2263: $i] : ( hBOOL @ ( hAPP @ SV625 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV202 ) @ SY2262 ) @ SY2263 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7032]) ).
thf(7214,plain,
! [SV202: $i,SV440: $i,SV625: $i] :
( ( ~ ! [SY2264: $i,SY2265: $i] : ( hBOOL @ ( hAPP @ SV625 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV202 ) @ SY2264 ) @ SY2265 ) ) )
| ! [SY2266: $i] : ( hBOOL @ ( hAPP @ SV625 @ SY2266 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7033]) ).
thf(7215,plain,
! [SV203: $i,SV441: $i,SV626: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV441 ) @ SV203 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV203 ) @ SV441 ) )
| ( SV203 = SV441 ) )
| ~ ( ( SV203 != SV441 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV203 ) @ SV441 ) ) ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV626 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7034]) ).
thf(7216,plain,
! [SV204: $i,SV442: $i,SV627: $i,SV758: $i,SV829: $i,SV869: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV869 @ ( tc_fun @ SV829 @ tc_HOL_Obool ) ) ) @ SV758 ) @ SV627 ) @ SV442 ) @ SV204 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV758 @ SV442 ) @ SV204 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV627 @ SV442 ) @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7035]) ).
thf(7217,plain,
! [SV629: $i,SV207: $i,SV445: $i] :
( ( ( SV445 != SV207 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV629 ) @ SV445 ) @ SV207 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV629 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7037]) ).
thf(7218,plain,
! [SV208: $i,SV446: $i,SV630: $i,SV759: $i,SV830: $i,SV870: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV870 @ SV830 ) @ SV759 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV630 @ ( tc_fun @ SV446 @ tc_HOL_Obool ) ) ) @ SV870 ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV208 @ SV830 ) @ SV759 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7038]) ).
thf(7219,plain,
! [SV209: $i,SV447: $i,SV631: $i,SV760: $i,SV831: $i] :
( ( ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SV831 @ SV760 @ SV631 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV631 @ SV447 ) @ ( hAPP @ ( hAPP @ SV631 @ SV447 ) @ SV209 ) )
= ( hAPP @ ( hAPP @ SV631 @ SV447 ) @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7039]) ).
thf(7220,plain,
! [SV450: $i,SV212: $i,SV633: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV633 @ tc_HOL_Obool ) ) @ SV212 ) @ SV450 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV633 ) @ SV212 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV633 ) @ SV450 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7040]) ).
thf(7221,plain,
! [SV213: $i,SV451: $i,SV634: $i,SV761: $i] :
( ( ( class_Orderings_Oorder @ SV761 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV761 ) @ SV634 ) @ SV451 ) )
| ( SV634 != SV213 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV761 ) @ SV213 ) @ SV451 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7041]) ).
thf(7222,plain,
! [SV635: $i,SV214: $i,SV452: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV452 ) @ SV214 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV635 ) @ SV214 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV635 ) @ SV452 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7042]) ).
thf(7223,plain,
! [SV215: $i,SV453: $i,SV636: $i,SV762: $i] :
( ( ( SV762 = SV636 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV636 ) @ SV215 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV762 ) @ SV215 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7043]) ).
thf(7224,plain,
! [SV216: $i,SV454: $i,SV637: $i,SV763: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV763 ) @ SV637 ) @ SV454 ) @ SV216 ) )
| ( SV637 = SV216 )
| ( hBOOL @ ( hAPP @ SV454 @ SV216 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7044]) ).
thf(7225,plain,
! [SV763: $i,SV454: $i,SV216: $i,SV637: $i] :
( ( ~ ( ~ ( ( SV637 = SV216 )
| ( hBOOL @ ( hAPP @ SV454 @ SV216 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV763 ) @ SV637 ) @ SV454 ) @ SV216 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7044]) ).
thf(7226,plain,
! [SV217: $i,SV455: $i,SV638: $i,SV764: $i,SV832: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
| ~ ! [SY2491: $i] :
~ ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SY2491 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2491 ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SY2491 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2491 ) @ SV217 ) ) ) ) )
| ~ ( ~ ~ ! [SY2492: $i] :
~ ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SY2492 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2492 ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SY2492 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2492 ) @ SV217 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7045]) ).
thf(7227,plain,
! [SV218: $i,SV456: $i] :
( ( ( ~ ( class_Finite__Set_Ofinite @ SV456 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite @ SV218 ) )
= $true )
| ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV456 @ SV218 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7046]) ).
thf(7228,plain,
! [SV219: $i,SV457: $i,SV639: $i,SV765: $i,SV833: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV833 @ SV765 @ SV639 ) @ SV457 ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV639 @ SV219 ) @ SV457 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7047]) ).
thf(7229,plain,
! [SV221: $i,SV459: $i,SV641: $i,SV766: $i] :
( ( ( c_Equiv__Relations_Oequivp @ SV766 @ SV641 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV641 @ SV459 ) @ SV221 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV641 @ SV221 ) @ SV459 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7049]) ).
thf(7230,plain,
! [SV223: $i,SV461: $i,SV642: $i,SV767: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV767 @ SV642 @ SV461 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV767 ) @ tc_HOL_Obool ) ) @ SV223 ) @ SV461 ) )
| ( c_Hoare__Mirabelle_Ohoare__derivs @ SV767 @ SV642 @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7050]) ).
thf(7231,plain,
! [SV224: $i,SV462: $i,SV643: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV643 ) @ SV462 )
!= SV224 )
| ( SV462
= ( hAPP @ ( c_List_Orev @ SV643 ) @ SV224 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7051]) ).
thf(7232,plain,
! [SV224: $i,SV643: $i,SV462: $i] :
( ( ( SV462
!= ( hAPP @ ( c_List_Orev @ SV643 ) @ SV224 ) )
| ( ( hAPP @ ( c_List_Orev @ SV643 ) @ SV462 )
= SV224 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7052]) ).
thf(7233,plain,
! [SV225: $i,SV463: $i,SV644: $i,SV768: $i,SV834: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequivp @ SV834 @ SV768 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV644 ) @ SV463 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV463 ) @ SV225 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV644 ) @ SV225 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7053]) ).
thf(7234,plain,
! [SV226: $i,SV464: $i,SV645: $i,SV769: $i,SV835: $i,SV871: $i] :
( ( ! [SY2520: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY2520 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
| ~ ! [SY2430: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SY2430 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2430 ) @ SV226 ) ) ) )
| ~ ( ~ ~ ! [SY2431: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SY2431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2431 ) @ SV226 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY2520 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7054]) ).
thf(7235,plain,
! [SV227: $i,SV465: $i,SV646: $i,SV770: $i,SV836: $i,SV872: $i] :
( ( ! [SY2523: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY2523 @ SV872 @ SV836 @ SV770 @ SV646 @ SV465 )
| ( ( hAPP @ ( hAPP @ SV836 @ SV227 ) @ SV227 )
= SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7055]) ).
thf(7236,plain,
! [SV228: $i,SV466: $i,SV647: $i,SV771: $i,SV837: $i,SV873: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV873 @ SV837 ) @ SV771 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV647 @ ( tc_fun @ SV466 @ tc_HOL_Obool ) ) ) @ SV873 ) @ SV228 ) @ SV837 ) @ SV771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7056]) ).
thf(7237,plain,
! [SV229: $i,SV467: $i,SV648: $i,SV772: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV772 ) @ SV648 ) @ SV467 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV772 @ tc_HOL_Obool ) ) @ SV467 ) @ SV229 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV772 ) @ SV648 ) @ SV229 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7057]) ).
thf(7238,plain,
! [SV230: $i,SV468: $i,SV649: $i,SV773: $i] :
( ( ( class_Orderings_Oorder @ SV773 )
= $false )
| ( ( ( SV649 != SV468 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV773 ) @ SV230 ) @ SV468 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV773 ) @ SV230 ) @ SV649 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7058]) ).
thf(7239,plain,
! [SV231: $i,SV469: $i,SV650: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV650 ) @ SV469 ) @ SV231 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV650 ) @ SV231 ) @ SV469 ) )
| ( SV231 = SV469 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV650 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7059]) ).
thf(7240,plain,
! [SV233: $i,SV471: $i,SV651: $i,SV774: $i,SV838: $i,SV874: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV874 @ SV838 ) @ SV774 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV651 @ ( tc_fun @ SV471 @ tc_HOL_Obool ) ) ) @ SV233 ) @ SV874 ) @ SV838 ) @ SV774 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7060]) ).
thf(7241,plain,
! [SV234: $i,SV472: $i,SV652: $i,SV775: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV775 @ tc_HOL_Obool ) ) @ SV652 ) @ SV472 ) @ SV234 ) )
= $false )
| ( ( ~ ~ ( hBOOL @ ( hAPP @ SV652 @ SV234 ) )
| ( hBOOL @ ( hAPP @ SV472 @ SV234 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7061]) ).
thf(7242,plain,
! [SV235: $i,SV473: $i,SV653: $i,SV776: $i,SV839: $i,SV875: $i] :
( ( ! [SY2524: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2524 @ SV875 @ SV839 @ SV776 @ SV653 )
| ~ ( ~ ( ( ( hAPP @ SV839 @ SV473 )
!= ( hAPP @ SV839 @ SV235 ) )
| ( SV473 = SV235 ) )
| ~ ( ( SV473 != SV235 )
| ( ( hAPP @ SV839 @ SV473 )
= ( hAPP @ SV839 @ SV235 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7062]) ).
thf(7243,plain,
! [SV236: $i,SV474: $i,SV654: $i,SV777: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV777 @ tc_HOL_Obool ) ) @ SV654 ) @ SV474 ) @ SV236 ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV654 @ SV236 ) )
| ~ ( hBOOL @ ( hAPP @ SV474 @ SV236 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7063]) ).
thf(7244,plain,
! [SV238: $i,SV476: $i,SV656: $i,SV778: $i,SV840: $i,SV876: $i] :
( ( ~ ( c_Typedef_Otype__definition @ SV876 @ SV840 @ SV778 @ SV656 @ SV476 )
| ( ( hAPP @ SV656 @ ( hAPP @ SV778 @ SV238 ) )
= SV238 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7065]) ).
thf(7245,plain,
! [SV239: $i,SV877: $i,SV477: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV477 @ SV877 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV477 @ ( c_Hilbert__Choice_OEps @ SV239 @ SV477 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[7066]) ).
thf(7246,plain,
! [SV240: $i,SV478: $i,SV657: $i,SV779: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV779 @ tc_HOL_Obool ) ) @ SV657 ) @ SV478 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV779 @ tc_HOL_Obool ) ) @ SV657 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV779 ) @ SV240 ) @ SV478 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7067]) ).
thf(7247,plain,
! [SV479: $i,SV241: $i,SV658: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV658 @ tc_HOL_Obool ) ) @ SV241 ) @ SV479 ) ) )
= $true )
| ( ( SV479 = SV241 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV658 @ tc_HOL_Obool ) ) @ SV479 ) @ SV241 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7068]) ).
thf(7248,plain,
! [SV480: $i,SV242: $i,SV659: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV659 @ ( tc_fun @ SV659 @ tc_HOL_Obool ) ) ) @ SV242 ) @ SV480 ) ) )
= $true )
| ( ( c_Wellfounded_OwfP @ SV659 @ SV242 )
= $true )
| ( ( c_Wellfounded_OwfP @ SV659 @ SV480 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7069]) ).
thf(7249,plain,
! [SV660: $i,SV243: $i,SV481: $i] :
( ( ( ~ ( ( SV481 != SV243 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) ) )
| ( SV481 = SV243 ) ) )
= $false )
| ( ( class_Orderings_Oorder @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7070]) ).
thf(7250,plain,
! [SV34: $i,SV276: $i,SV502: $i,SV669: $i,SV782: $i,SV842: $i,SV878: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SV878 @ SV842 @ SV782 @ SV669 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV502 @ SV878 @ SV782 @ SV276 ) @ SV34 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV502 @ SV842 @ SV782 @ ( hAPP @ ( c_Fun_Ocomp @ SV878 @ SV842 @ SV502 @ SV669 ) @ SV276 ) ) @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7072]) ).
thf(7251,plain,
! [SV40: $i,SV282: $i,SV505: $i,SV672: $i,SV784: $i,SV844: $i,SV879: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV879 @ SV844 @ SV784 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV879 @ SV672 @ SV844 ) @ SV505 ) @ SV282 ) ) @ SV40 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV879 @ SV672 @ SV784 ) @ SV505 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV672 @ SV844 @ SV784 ) @ SV282 ) @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7074]) ).
thf(7252,plain,
! [SV680: $i,SV65: $i,SV515: $i,SV304: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV304 @ SV515 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV65 @ tc_HOL_Obool ) ) @ SV680 ) @ SV304 ) @ SV515 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV680 @ SV515 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7080]) ).
thf(7253,plain,
! [SV67: $i,SV306: $i,SV517: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 )
= SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7082]) ).
thf(7254,plain,
! [SV67: $i,SV306: $i,SV517: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 )
!= SV67 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7083]) ).
thf(7255,plain,
! [SV69: $i,SV308: $i,SV519: $i,SV682: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV682 @ SV519 @ SV308 ) @ SV69 ) )
| ~ ! [SY1684: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ SY1684 ) @ SV69 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7085]) ).
thf(7256,plain,
! [SV519: $i,SV682: $i,SV69: $i,SV308: $i] :
( ( ~ ~ ! [SY1685: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ SY1685 ) @ SV69 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV682 @ SV519 @ SV308 ) @ SV69 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7086]) ).
thf(7257,plain,
! [SV70: $i,SV309: $i] :
( ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false )
| ( ( ~ ( ~ ~ ! [SY1062: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1062 ) @ SY1062 ) )
| ~ ! [SY1063: $i,SY1064: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1064 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1064 ) @ SY1064 ) ) )
| ( ( hAPP @ SV70 @ SY1063 )
!= ( hAPP @ SV70 @ SY1064 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1064 ) @ SY1064 ) ) )
| ( ( hAPP @ SV70 @ SY1063 )
!= ( hAPP @ SV70 @ SY1064 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1064 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7087]) ).
thf(7258,plain,
! [SV309: $i,SV70: $i] :
( ( ( ~ ( ~ ~ ! [SY1065: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1065 ) @ SY1065 ) )
| ~ ! [SY1066: $i,SY1067: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7088]) ).
thf(7259,plain,
! [SV520: $i,SV683: $i,SV71: $i,SV310: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV683 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV520 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV520 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV683 ) ) ) )
= $false )
| ( ( SV683 = SV520 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7089]) ).
thf(7260,plain,
! [SV73: $i,SV312: $i,SV521: $i,SV684: $i,SV789: $i,SV848: $i,SV880: $i] :
( ( ! [SY2525: $i,SY2526: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2526 @ SY2525 @ SV880 @ SV848 ) @ SV789 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV684 @ SY2525 @ SV880 @ SV521 ) @ SV312 ) )
| ( ( hAPP @ SV848 @ ( hAPP @ SV789 @ SV73 ) )
= ( hAPP @ SV521 @ ( hAPP @ SV312 @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7090]) ).
thf(7261,plain,
! [SV74: $i,SV313: $i,SV522: $i,SV685: $i] :
( ( ( ~ ! [SY2341: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV685 ) @ ( hAPP @ SV522 @ SY2341 ) ) @ ( hAPP @ SV313 @ SY2341 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV74 @ SV685 ) ) @ SV522 ) @ SV313 ) )
= $true )
| ( ( class_Orderings_Oord @ SV685 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7091]) ).
thf(7262,plain,
! [SV75: $i,SV314: $i,SV523: $i,SV686: $i,SV790: $i,SV849: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV849 @ SV790 ) @ SV686 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV523 @ SV790 ) @ SV686 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV314 @ ( tc_fun @ SV75 @ tc_HOL_Obool ) ) ) @ SV849 ) @ SV523 ) @ SV790 ) @ SV686 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7092]) ).
thf(7263,plain,
! [SV315: $i,SV524: $i,SV77: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV77 @ tc_HOL_Obool ) ) @ SV524 ) @ SV315 ) ) )
= $false )
| ( ( SV524 = SV315 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7093]) ).
thf(7264,plain,
! [SV524: $i,SV315: $i,SV77: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV77 @ tc_HOL_Obool ) ) @ SV315 ) @ SV524 ) ) )
= $false )
| ( ( SV524 = SV315 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7093]) ).
thf(7265,plain,
! [SV84: $i,SV322: $i,SV528: $i,SV688: $i,SV791: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV791 @ tc_HOL_Obool ) ) @ SV688 ) @ SV528 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV322 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV322 @ SV791 @ SV84 ) @ SV688 ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV322 @ SV791 @ SV84 ) @ SV528 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7095]) ).
thf(7266,plain,
! [SV85: $i,SV323: $i,SV881: $i,SV529: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV529 @ SV881 ) ) )
= $true )
| ( ( ( SV323
!= ( c_Hilbert__Choice_OEps @ SV85 @ SV529 ) )
| ( hBOOL @ ( hAPP @ SV529 @ SV323 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[7096]) ).
thf(7267,plain,
! [SV530: $i,SV689: $i,SV86: $i,SV324: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) ) ) )
= $true )
| ( ( SV689 = SV530 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7097]) ).
thf(7268,plain,
! [SV531: $i,SV87: $i,SV325: $i,SV690: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV690 @ tc_HOL_Obool ) ) @ SV325 ) @ SV87 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV690 @ tc_HOL_Obool ) ) @ SV531 ) @ SV87 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV690 @ tc_HOL_Obool ) ) @ SV531 ) @ SV325 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7098]) ).
thf(7269,plain,
! [SV88: $i,SV326: $i,SV532: $i,SV691: $i,SV792: $i,SV850: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV850 @ ( tc_fun @ SV792 @ tc_HOL_Obool ) ) ) @ SV691 ) @ SV532 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV691 @ SV326 ) @ SV88 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV532 @ SV326 ) @ SV88 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7099]) ).
thf(7270,plain,
! [SV89: $i,SV327: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ SV327 )
= ( hAPP @ c_Int_ORep__Integ @ SV89 ) )
= $false )
| ( ( SV327 = SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7100]) ).
thf(7271,plain,
! [SV89: $i,SV327: $i] :
( ( ( SV327 = SV89 )
= $false )
| ( ( ( hAPP @ c_Int_ORep__Integ @ SV327 )
= ( hAPP @ c_Int_ORep__Integ @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7101]) ).
thf(7272,plain,
! [SV90: $i,SV328: $i,SV533: $i,SV692: $i,SV793: $i,SV851: $i] :
( ( ( ~ ( ( SV851 != SV793 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV692 @ SV533 @ SV328 @ SV793 @ SV90 ) @ SV851 )
= ( hAPP @ SV328 @ SV851 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7102]) ).
thf(7273,plain,
! [SV91: $i,SV329: $i,SV534: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV534 ) @ SV329 )
!= ( hAPP @ ( c_List_Orev @ SV534 ) @ SV91 ) )
= $true )
| ( ( SV329 = SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7103]) ).
thf(7274,plain,
! [SV534: $i,SV91: $i,SV329: $i] :
( ( ( SV329 != SV91 )
= $true )
| ( ( ( hAPP @ ( c_List_Orev @ SV534 ) @ SV329 )
= ( hAPP @ ( c_List_Orev @ SV534 ) @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7104]) ).
thf(7275,plain,
! [SV92: $i,SV330: $i,SV535: $i,SV693: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV693 @ SV535 @ SV330 ) @ SV92 ) )
| ~ ! [SY1733: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ SY1733 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7105]) ).
thf(7276,plain,
! [SV535: $i,SV693: $i,SV92: $i,SV330: $i] :
( ( ~ ~ ! [SY1734: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ SY1734 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV693 @ SV535 @ SV330 ) @ SV92 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7106]) ).
thf(7277,plain,
! [SV95: $i,SV333: $i,SV537: $i,SV694: $i,SV794: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ SV694 ) @ SV537 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ SV333 ) @ SV95 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ SV694 ) @ SV333 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ SV537 ) @ SV95 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7107]) ).
thf(7278,plain,
! [SV96: $i,SV334: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV334 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV96 ) )
= $false )
| ( ( SV334 = SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7108]) ).
thf(7279,plain,
! [SV96: $i,SV334: $i] :
( ( ( SV334 = SV96 )
= $false )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV334 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7109]) ).
thf(7280,plain,
! [SV97: $i,SV335: $i,SV538: $i,SV695: $i,SV795: $i,SV852: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV852 @ ( tc_fun @ SV795 @ tc_HOL_Obool ) ) ) @ SV695 ) @ SV538 ) @ SV335 ) @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV695 @ SV335 ) @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7110]) ).
thf(7281,plain,
! [SV99: $i,SV337: $i,SV540: $i,SV696: $i,SV796: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV796 @ SV696 @ SV540 ) @ SV337 ) @ SV99 ) )
| ( hBOOL @ ( hAPP @ SV337 @ ( hAPP @ SV540 @ SV99 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7111]) ).
thf(7282,plain,
! [SV696: $i,SV796: $i,SV99: $i,SV540: $i,SV337: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV337 @ ( hAPP @ SV540 @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV796 @ SV696 @ SV540 ) @ SV337 ) @ SV99 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7111]) ).
thf(7283,plain,
! [SV100: $i,SV338: $i,SV541: $i,SV697: $i,SV797: $i,SV853: $i,SV882: $i] :
( ( ! [SY2527: $i,SY2528: $i,SY2529: $i,SY2530: $i] :
( ( ( hAPP @ SY2530 @ ( hAPP @ SY2529 @ SY2528 ) )
!= ( hAPP @ SY2527 @ ( hAPP @ SV882 @ SV853 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV797 @ SV697 @ SV541 @ SY2530 ) @ SY2529 ) @ SY2528 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV338 @ SV697 @ SV100 @ SY2527 ) @ SV882 ) @ SV853 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7112]) ).
thf(7284,plain,
! [SV101: $i,SV339: $i,SV542: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV339 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) @ SV339 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7113]) ).
thf(7285,plain,
! [SV339: $i,SV101: $i,SV542: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) @ SV339 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV339 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7114]) ).
thf(7286,plain,
! [SV102: $i,SV340: $i,SV543: $i,SV698: $i,SV798: $i,SV854: $i] :
( ( ( ~ ( c_Finite__Set_Ofun__left__comm @ SV854 @ SV798 @ SV698 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV698 @ SV543 ) @ ( hAPP @ ( hAPP @ SV698 @ SV340 ) @ SV102 ) )
= ( hAPP @ ( hAPP @ SV698 @ SV340 ) @ ( hAPP @ ( hAPP @ SV698 @ SV543 ) @ SV102 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7115]) ).
thf(7287,plain,
! [SV103: $i,SV341: $i,SV544: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV103 ) ) )
= $true )
| ( ( ! [SY2145: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SY2145 ) @ SV103 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SY2145 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7116]) ).
thf(7288,plain,
! [SV544: $i,SV103: $i,SV341: $i] :
( ( ( ~ ! [SY2146: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SY2146 ) @ SV103 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SY2146 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7117]) ).
thf(7289,plain,
! [SV105: $i,SV343: $i,SV546: $i,SV699: $i,SV799: $i] :
( ( ( c_Equiv__Relations_Opart__equivp @ SV799 @ SV699 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV546 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV343 ) @ SV105 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV546 ) @ SV105 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7118]) ).
thf(7290,plain,
! [SV108: $i,SV855: $i,SV346: $i] :
( ( ( hBOOL @ ( hAPP @ SV346 @ SV855 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV346 @ ( c_Hilbert__Choice_OEps @ SV108 @ SV346 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7119]) ).
thf(7291,plain,
! [SV109: $i,SV347: $i,SV547: $i,SV700: $i,SV800: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV800 @ SV700 ) @ SV547 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV347 @ SV109 @ SV800 ) @ SV547 ) @ SV700 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7120]) ).
thf(7292,plain,
! [SV110: $i,SV348: $i,SV548: $i,SV701: $i,SV801: $i] :
( ( ~ ( ( ( c_Fun_Ofun__upd @ SV801 @ SV701 @ SV548 @ SV348 @ SV110 )
!= SV548 )
| ( ( hAPP @ SV548 @ SV348 )
= SV110 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7121]) ).
thf(7293,plain,
! [SV701: $i,SV801: $i,SV110: $i,SV348: $i,SV548: $i] :
( ( ~ ( ( ( hAPP @ SV548 @ SV348 )
!= SV110 )
| ( ( c_Fun_Ofun__upd @ SV801 @ SV701 @ SV548 @ SV348 @ SV110 )
= SV548 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7121]) ).
thf(7294,plain,
! [SV112: $i,SV350: $i,SV550: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV112 ) ) )
= $true )
| ( ( ! [SY2153: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV350 @ SY2153 ) @ SV112 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SY2153 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7122]) ).
thf(7295,plain,
! [SV550: $i,SV112: $i,SV350: $i] :
( ( ( ~ ! [SY2154: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV350 @ SY2154 ) @ SV112 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SY2154 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7123]) ).
thf(7296,plain,
! [SV702: $i,SV113: $i,SV351: $i,SV551: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV551 @ SV351 ) @ SV113 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV551 @ SV113 ) @ SV351 ) )
= $true )
| ( ( c_Predicate_Osymp @ SV702 @ SV551 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7124]) ).
thf(7297,plain,
! [SV114: $i,SV352: $i,SV552: $i,SV703: $i,SV802: $i,SV856: $i] :
( ( ~ ( ( SV856 != SV802 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV703 @ SV552 @ SV352 @ SV802 @ SV114 ) @ SV856 )
= SV114 ) )
| ~ ( ~ ( ( SV856 != SV802 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV703 @ SV552 @ SV352 @ SV802 @ SV114 ) @ SV856 )
= ( hAPP @ SV352 @ SV856 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7125]) ).
thf(7298,plain,
! [SV353: $i,SV115: $i,SV553: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV553 ) @ SV115 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV553 ) @ SV353 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV553 @ tc_HOL_Obool ) ) @ SV353 ) @ SV115 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7126]) ).
thf(7299,plain,
! [SV116: $i,SV354: $i] :
( ( ( class_Enum_Oenum @ SV354 )
= $false )
| ( ( ~ ( class_Enum_Oenum @ SV116 ) )
= $true )
| ( ( class_Enum_Oenum @ ( tc_fun @ SV354 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7127]) ).
thf(7300,plain,
! [SV117: $i,SV355: $i,SV554: $i,SV704: $i,SV803: $i,SV857: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV704 ) @ SV554 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV355 ) @ SV117 ) )
| ~ ( ( SV704 != SV355 )
| ( SV554 != SV117 ) ) )
| ~ ( ~ ~ ( ( SV704 != SV355 )
| ( SV554 != SV117 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV704 ) @ SV554 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV355 ) @ SV117 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7128]) ).
thf(7301,plain,
! [SV119: $i,SV357: $i,SV555: $i,SV705: $i,SV804: $i,SV858: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV858 @ ( tc_fun @ SV804 @ tc_HOL_Obool ) ) ) @ SV705 ) @ SV555 ) @ SV357 ) @ SV119 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV555 @ SV357 ) @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7130]) ).
thf(7302,plain,
! [SV120: $i,SV358: $i,SV556: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
| ( SV358 = SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7131]) ).
thf(7303,plain,
! [SV120: $i,SV358: $i,SV556: $i] :
( ( ( ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
| ( SV358 = SV120 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7132]) ).
thf(7304,plain,
! [SV121: $i,SV359: $i,SV706: $i,SV557: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV557 @ SV706 ) ) @ SV359 ) @ SV121 ) )
| ! [SY2373: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV706 ) @ ( hAPP @ SV359 @ SY2373 ) ) @ ( hAPP @ SV121 @ SY2373 ) ) ) )
| ~ ( ~ ! [SY2374: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV706 ) @ ( hAPP @ SV359 @ SY2374 ) ) @ ( hAPP @ SV121 @ SY2374 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV557 @ SV706 ) ) @ SV359 ) @ SV121 ) ) ) )
= $false )
| ( ( class_Orderings_Oord @ SV706 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7133]) ).
thf(7305,plain,
! [SV123: $i,SV361: $i] :
( ( ( hBOOL @ ( hAPP @ SV361 @ ( c_Hilbert__Choice_OEps @ SV123 @ SV361 ) ) )
= $false )
| ( ( ~ ! [SY1800: $i] :
~ ( hBOOL @ ( hAPP @ SV361 @ SY1800 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7134]) ).
thf(7306,plain,
! [SV123: $i,SV361: $i] :
( ( ( ~ ! [SY1801: $i] :
~ ( hBOOL @ ( hAPP @ SV361 @ SY1801 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV361 @ ( c_Hilbert__Choice_OEps @ SV123 @ SV361 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7135]) ).
thf(7307,plain,
! [SV125: $i,SV363: $i,SV559: $i,SV707: $i,SV805: $i] :
( ( ( c_Fun_Oinj__on @ SV805 @ SV707 @ SV559 @ SV363 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV805 @ tc_HOL_Obool ) ) @ SV125 ) @ SV363 ) )
| ( c_Fun_Oinj__on @ SV805 @ SV707 @ SV559 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7136]) ).
thf(7308,plain,
! [SV126: $i,SV708: $i,SV364: $i,SV560: $i] :
( ( ( SV560 != SV364 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV708 ) @ SV364 ) @ SV126 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV708 ) @ SV560 ) @ SV126 ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV708 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7137]) ).
thf(7309,plain,
! [SV127: $i,SV365: $i,SV561: $i,SV709: $i,SV806: $i,SV859: $i,SV883: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV883 @ SV859 @ SV806 @ SV709 ) @ SV561 )
!= SV365 )
| ( ( hAPP @ SV709 @ ( hAPP @ SV561 @ SV127 ) )
= ( hAPP @ SV365 @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7138]) ).
thf(7310,plain,
! [SV128: $i,SV366: $i,SV562: $i,SV710: $i,SV807: $i,SV860: $i] :
( ( ~ ( ( SV860 != SV807 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV710 @ SV562 @ SV366 @ SV807 @ SV128 ) @ SV860 )
= SV128 ) )
| ~ ( ~ ( ( SV860 != SV807 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV710 @ SV562 @ SV366 @ SV807 @ SV128 ) @ SV860 )
= ( hAPP @ SV366 @ SV860 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7139]) ).
thf(7311,plain,
! [SV129: $i,SV367: $i,SV563: $i,SV711: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV367 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV129 ) )
| ( SV367 = SV129 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7140]) ).
thf(7312,plain,
! [SV563: $i,SV711: $i,SV129: $i,SV367: $i] :
( ( ( SV367 != SV129 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV367 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV129 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7141]) ).
thf(7313,plain,
! [SV130: $i,SV368: $i,SV564: $i,SV712: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV712 ) @ SV564 ) @ SV368 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV712 ) @ SV368 ) @ SV130 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV712 ) @ SV564 ) @ SV130 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV712 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7142]) ).
thf(7314,plain,
! [SV565: $i,SV131: $i,SV713: $i,SV369: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV713 ) @ SV131 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV565 ) @ SV131 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV565 ) @ SV131 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV713 ) @ SV131 ) ) ) )
= $false )
| ( ( SV713 = SV565 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7143]) ).
thf(7315,plain,
! [SV132: $i,SV370: $i,SV566: $i,SV714: $i,SV808: $i,SV861: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV861 ) @ SV808 ) @ SV714 )
!= SV566 )
= $true )
| ( ( ( SV370
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV861 ) @ SV714 ) @ SV132 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV861 ) @ SV808 ) @ SV370 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV861 ) @ SV566 ) @ SV132 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7144]) ).
thf(7316,plain,
! [SV133: $i,SV371: $i,SV567: $i,SV715: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV567 ) @ SV371 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV133 ) @ SV371 ) )
| ( SV567 = SV133 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7145]) ).
thf(7317,plain,
! [SV371: $i,SV715: $i,SV133: $i,SV567: $i] :
( ( ( SV567 != SV133 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV567 ) @ SV371 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV133 ) @ SV371 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7146]) ).
thf(7318,plain,
! [SV716: $i,SV372: $i,SV134: $i,SV568: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV568 @ SV134 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV372 @ SV134 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV716 @ tc_HOL_Obool ) ) @ SV568 ) @ SV372 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7147]) ).
thf(7319,plain,
! [SV717: $i,SV135: $i,SV373: $i,SV569: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV569 @ SV373 ) @ SV135 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV569 @ SV135 ) @ SV373 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV717 @ SV569 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7148]) ).
thf(7320,plain,
! [SV374: $i,SV136: $i,SV570: $i,SV718: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV718 @ SV570 ) @ SV136 ) ) )
= $true )
| ( ( SV374 = SV136 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV718 @ SV570 ) @ SV374 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7149]) ).
thf(7321,plain,
! [SV137: $i,SV375: $i,SV571: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV571 ) @ SV375 ) @ SV137 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV137 @ SV375 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7150]) ).
thf(7322,plain,
! [SV571: $i,SV375: $i,SV137: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV137 @ SV375 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV571 ) @ SV375 ) @ SV137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7151]) ).
thf(7323,plain,
! [SV140: $i,SV378: $i,SV574: $i,SV719: $i,SV809: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV809 @ SV719 ) @ SV574 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV378 @ SV140 @ SV809 ) @ SV574 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7152]) ).
thf(7324,plain,
! [SV141: $i,SV379: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV379 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV141 ) )
= $false )
| ( ( SV379 = SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7153]) ).
thf(7325,plain,
! [SV141: $i,SV379: $i] :
( ( ( SV379 = SV141 )
= $false )
| ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV379 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7154]) ).
thf(7326,plain,
! [SV142: $i,SV380: $i,SV575: $i,SV720: $i,SV810: $i,SV862: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV862 @ ( tc_fun @ SV810 @ tc_HOL_Obool ) ) ) @ SV720 ) @ SV575 ) @ SV380 ) @ SV142 ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV720 @ SV380 ) @ SV142 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV575 @ SV380 ) @ SV142 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7155]) ).
thf(7327,plain,
! [SV381: $i,SV143: $i,SV576: $i,SV721: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV576 ) @ SV143 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV576 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV381 ) @ SV143 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV576 ) @ SV381 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7156]) ).
thf(7328,plain,
! [SV144: $i,SV382: $i,SV577: $i] :
( ( ( SV577 != SV382 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV577 ) @ SV382 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV382 ) @ SV577 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7157]) ).
thf(7329,plain,
! [SV382: $i,SV577: $i,SV144: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV577 ) @ SV382 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV382 ) @ SV577 ) ) ) )
= $true )
| ( ( SV577 = SV382 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7158]) ).
thf(7330,plain,
! [SV579: $i,SV146: $i,SV722: $i,SV384: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV384 @ tc_HOL_Obool ) ) @ SV722 ) @ SV146 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV146 @ SV579 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV722 @ SV579 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7159]) ).
thf(7331,plain,
! [SV580: $i,SV147: $i,SV385: $i,SV723: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV723 @ tc_HOL_Obool ) ) @ SV385 ) @ SV147 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV723 @ tc_HOL_Obool ) ) @ SV580 ) @ SV147 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV723 @ tc_HOL_Obool ) ) @ SV580 ) @ SV385 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7160]) ).
thf(7332,plain,
! [SV581: $i,SV148: $i,SV386: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV386 ) @ SV148 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV581 ) @ SV148 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV581 ) @ SV386 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7161]) ).
thf(7333,plain,
! [SV150: $i,SV388: $i,SV583: $i,SV725: $i,SV811: $i] :
( ( ( class_Orderings_Oord @ SV811 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV725 @ SV811 ) ) @ SV583 ) @ SV388 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV811 ) @ ( hAPP @ SV583 @ SV150 ) ) @ ( hAPP @ SV388 @ SV150 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7163]) ).
thf(7334,plain,
! [SV151: $i,SV389: $i,SV584: $i,SV726: $i,SV812: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV812 @ SV726 ) @ SV584 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV389 @ SV151 @ SV812 ) @ SV726 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7164]) ).
thf(7335,plain,
! [SV152: $i,SV390: $i,SV585: $i,SV727: $i,SV813: $i,SV863: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV863 @ SV813 ) @ SV727 ) @ SV585 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV863 @ SV813 ) @ SV390 ) @ SV152 ) )
= $true )
| ( ( ~ ( ( SV727 != SV390 )
| ( SV585 != SV152 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7165]) ).
thf(7336,plain,
! [SV391: $i,SV586: $i,SV153: $i,SV728: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV728 ) @ SV153 ) @ SV586 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV728 ) @ SV153 ) @ SV391 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV728 @ tc_HOL_Obool ) ) @ SV586 ) @ SV391 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7166]) ).
thf(7337,plain,
! [SV392: $i,SV587: $i,SV154: $i,SV729: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV729 ) @ SV154 ) @ SV587 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV729 ) @ SV154 ) @ SV392 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV729 @ tc_HOL_Obool ) ) @ SV587 ) @ SV392 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7167]) ).
thf(7338,plain,
! [SV155: $i,SV393: $i,SV588: $i,SV730: $i,SV814: $i,SV864: $i] :
( ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV864 @ SV814 ) @ SV730 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV588 @ SV814 ) @ SV730 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV393 @ ( tc_fun @ SV155 @ tc_HOL_Obool ) ) ) @ SV588 ) @ SV864 ) @ SV814 ) @ SV730 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7168]) ).
thf(7339,plain,
! [SV156: $i,SV394: $i,SV589: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
| ~ ( ( SV394 != SV156 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7169]) ).
thf(7340,plain,
! [SV156: $i,SV394: $i,SV589: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
| ~ ( ( SV394 != SV156 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7170]) ).
thf(7341,plain,
! [SV159: $i,SV397: $i,SV591: $i,SV732: $i,SV815: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV815 @ SV732 @ SV591 ) @ SV397 ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV591 @ SV159 ) @ SV397 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7172]) ).
thf(7342,plain,
! [SV732: $i,SV815: $i,SV397: $i,SV159: $i,SV591: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV591 @ SV159 ) @ SV397 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV815 @ SV732 @ SV591 ) @ SV397 ) @ SV159 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7172]) ).
thf(7343,plain,
! [SV160: $i,SV398: $i,SV592: $i,SV733: $i,SV816: $i] :
( ( ( c_Predicate_Otransp @ SV816 @ SV733 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV592 ) @ SV398 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV398 ) @ SV160 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV592 ) @ SV160 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7173]) ).
thf(7344,plain,
! [SV161: $i,SV399: $i,SV593: $i] :
( ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV399 )
!= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV161 ) )
= $true )
| ( ( SV399 = SV161 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7174]) ).
thf(7345,plain,
! [SV593: $i,SV161: $i,SV399: $i] :
( ( ( SV399 != SV161 )
= $true )
| ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV399 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7175]) ).
thf(7346,plain,
! [SV162: $i,SV400: $i,SV594: $i,SV734: $i,SV817: $i] :
( ( ( class_Orderings_Oord @ SV817 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV734 @ SV817 ) ) @ SV594 ) @ SV400 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV817 ) @ ( hAPP @ SV594 @ SV162 ) ) @ ( hAPP @ SV400 @ SV162 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7176]) ).
thf(7347,plain,
! [SV163: $i,SV401: $i,SV595: $i,SV735: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV735 ) @ SV595 ) @ SV401 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV735 ) @ SV163 ) @ SV595 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV735 ) @ SV163 ) @ SV401 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV735 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7177]) ).
thf(7348,plain,
! [SV164: $i,SV402: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV402 )
= ( hAPP @ c_Nat_OSuc @ SV164 ) )
= $false )
| ( ( SV402 = SV164 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7178]) ).
thf(7349,plain,
! [SV164: $i,SV402: $i] :
( ( ( SV402 = SV164 )
= $false )
| ( ( ( hAPP @ c_Nat_OSuc @ SV402 )
= ( hAPP @ c_Nat_OSuc @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7179]) ).
thf(7350,plain,
! [SV736: $i,SV403: $i,SV165: $i,SV596: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV596 @ SV165 ) @ SV403 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV736 @ SV596 ) @ SV165 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV736 @ SV596 ) @ SV403 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7180]) ).
thf(7351,plain,
! [SV166: $i,SV404: $i,SV597: $i,SV737: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV737 ) @ SV597 ) @ SV404 ) ) )
= $true )
| ( ( ( SV404 != SV166 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV737 ) @ SV597 ) @ SV166 ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV737 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7181]) ).
thf(7352,plain,
! [SV169: $i,SV407: $i,SV600: $i,SV739: $i,SV818: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
| ~ ! [SY2478: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SY2478 ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SY2478 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7183]) ).
thf(7353,plain,
! [SV407: $i,SV818: $i,SV739: $i,SV169: $i,SV600: $i] :
( ( ~ ( ~ ~ ! [SY2479: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SY2479 ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SY2479 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7183]) ).
thf(7354,plain,
! [SV170: $i,SV408: $i,SV601: $i,SV740: $i,SV819: $i,SV865: $i] :
( ( ( SV865 != SV819 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV740 @ SV601 @ SV408 ) @ SV170 ) @ SV865 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV740 @ SV601 @ SV408 ) @ SV170 ) @ SV819 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7184]) ).
thf(7355,plain,
! [SV409: $i,SV171: $i,SV602: $i,SV741: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV741 @ SV602 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV171 @ tc_HOL_Obool ) ) @ SV409 ) @ SV741 ) @ SV602 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7185]) ).
thf(7356,plain,
! [SV741: $i,SV171: $i,SV602: $i,SV409: $i] :
( ( ( hBOOL @ ( hAPP @ SV409 @ SV602 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV171 @ tc_HOL_Obool ) ) @ SV409 ) @ SV741 ) @ SV602 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7185]) ).
thf(7357,plain,
! [SV603: $i,SV172: $i,SV410: $i,SV742: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV742 @ tc_HOL_Obool ) ) @ SV410 ) @ SV172 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV742 @ tc_HOL_Obool ) ) @ SV410 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV742 @ tc_HOL_Obool ) ) @ SV172 ) @ SV603 ) )
= SV603 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV742 @ tc_HOL_Obool ) ) @ SV603 ) @ SV410 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7186]) ).
thf(7358,plain,
! [SV173: $i,SV411: $i,SV604: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV604 ) @ SV411 ) @ SV173 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV604 ) @ SV173 ) @ SV411 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV604 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7187]) ).
thf(7359,plain,
! [SV415: $i,SV606: $i,SV177: $i,SV744: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV744 ) @ SV177 ) @ SV606 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV744 ) @ SV177 ) @ SV415 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV744 @ tc_HOL_Obool ) ) @ SV606 ) @ SV415 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7189]) ).
thf(7360,plain,
! [SV178: $i,SV416: $i,SV607: $i,SV745: $i,SV820: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV745 ) @ SV607 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV416 ) @ SV178 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV745 ) @ SV416 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV607 ) @ SV178 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7190]) ).
thf(7361,plain,
! [SV179: $i,SV417: $i,SV608: $i,SV746: $i,SV821: $i,SV866: $i] :
( ( ( ~ ( ( SV866 != SV821 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ SV608 ) @ SV866 ) @ SV417 ) ) @ SV821 ) @ SV179 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ SV608 ) @ SV821 ) @ SV179 ) ) @ SV866 ) @ SV417 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7191]) ).
thf(7362,plain,
! [SV180: $i,SV418: $i,SV609: $i,SV747: $i,SV822: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV747 ) @ SV609 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV418 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ SV822 @ SV418 @ SV180 ) @ SV747 ) ) @ ( hAPP @ ( c_Set_Oimage @ SV822 @ SV418 @ SV180 ) @ SV609 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7192]) ).
thf(7363,plain,
! [SV181: $i,SV419: $i,SV610: $i,SV748: $i,SV823: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV823 @ SV748 @ SV610 ) @ SV419 ) @ SV181 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV610 @ SV181 ) @ SV419 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7193]) ).
thf(7364,plain,
! [SV748: $i,SV823: $i,SV419: $i,SV181: $i,SV610: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV610 @ SV181 ) @ SV419 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV823 @ SV748 @ SV610 ) @ SV419 ) @ SV181 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7193]) ).
thf(7365,plain,
! [SV182: $i,SV420: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV420 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV182 ) )
= $false )
| ( ( SV420 = SV182 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7194]) ).
thf(7366,plain,
! [SV182: $i,SV420: $i] :
( ( ( SV420 = SV182 )
= $false )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV420 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7195]) ).
thf(7367,plain,
! [SV183: $i,SV421: $i,SV611: $i,SV749: $i,SV824: $i,SV867: $i,SV884: $i] :
( ( ! [SY2531: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2531 @ SV884 @ SV867 @ SV824 ) @ SV749 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV611 @ SV884 @ SV867 @ SV421 ) @ SV183 ) )
| ! [SY2485: $i] :
( ( hAPP @ SV824 @ ( hAPP @ SV749 @ SY2485 ) )
= ( hAPP @ SV421 @ ( hAPP @ SV183 @ SY2485 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7196]) ).
thf(7368,plain,
! [SV184: $i,SV422: $i] :
( ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $false )
| ( ( ! [SY1423: $i,SY1424: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1423 ) @ SY1424 ) )
| ( ( hAPP @ SV184 @ SY1423 )
= ( hAPP @ SV184 @ SY1424 ) ) )
| ~ ( ( ( hAPP @ SV184 @ SY1423 )
!= ( hAPP @ SV184 @ SY1424 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1423 ) @ SY1424 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7197]) ).
thf(7369,plain,
! [SV422: $i,SV184: $i] :
( ( ( ! [SY1425: $i,SY1426: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1425 ) @ SY1426 ) )
| ( ( hAPP @ SV184 @ SY1425 )
= ( hAPP @ SV184 @ SY1426 ) ) )
| ~ ( ( ( hAPP @ SV184 @ SY1425 )
!= ( hAPP @ SV184 @ SY1426 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SY1425 ) @ SY1426 ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7198]) ).
thf(7370,plain,
! [SV185: $i,SV423: $i,SV612: $i,SV750: $i,SV825: $i] :
( ( ( ( hAPP @ SV825 @ SV750 )
= SV612 )
= $false )
| ( ( ( c_Fun_Ofun__upd @ SV423 @ SV185 @ SV825 @ SV750 @ SV612 )
= SV825 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7199]) ).
thf(7371,plain,
! [SV186: $i,SV424: $i,SV613: $i,SV751: $i,SV826: $i,SV868: $i,SV885: $i] :
( ( ! [SY2533: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2533 @ SV885 ) @ SV868 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV826 @ SV868 ) @ SV751 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV613 @ SV424 @ SV186 @ SY2533 @ SV826 ) @ SV885 ) @ SV751 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7200]) ).
thf(7372,plain,
! [SV187: $i,SV425: $i,SV614: $i,SV752: $i,SV827: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV752 ) @ SV614 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV425 ) @ SV187 ) )
| ~ ( ( SV752 != SV425 )
| ( SV614 != SV187 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7201]) ).
thf(7373,plain,
! [SV827: $i,SV187: $i,SV614: $i,SV425: $i,SV752: $i] :
( ( ~ ( ~ ~ ( ( SV752 != SV425 )
| ( SV614 != SV187 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV752 ) @ SV614 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV425 ) @ SV187 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7201]) ).
thf(7374,plain,
! [SV616: $i,SV191: $i,SV429: $i,SV753: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SV429 ) @ SV191 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SV616 ) @ SV191 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SV616 ) @ SV429 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7203]) ).
thf(7375,plain,
! [SV192: $i,SV430: $i,SV617: $i,SV754: $i,SV828: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ SV754 ) @ SV617 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ SV430 ) @ SV192 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ SV754 ) @ SV192 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ SV617 ) @ SV430 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7204]) ).
thf(7376,plain,
! [SV620: $i,SV196: $i,SV434: $i,SV755: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV755 @ tc_HOL_Obool ) ) @ SV434 ) @ SV196 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV755 @ tc_HOL_Obool ) ) @ SV620 ) @ SV196 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV755 @ tc_HOL_Obool ) ) @ SV620 ) @ SV434 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7205]) ).
thf(7377,plain,
! [SV197: $i,SV435: $i,SV621: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV621 @ SV435 ) @ SV197 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV435 @ SV197 ) @ SV197 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7206]) ).
thf(7378,plain,
! [SV621: $i,SV197: $i,SV435: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV435 @ SV197 ) @ SV197 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV621 @ SV435 ) @ SV197 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7207]) ).
thf(7379,plain,
! [SV198: $i,SV436: $i,SV622: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV622 ) @ SV436 ) @ SV198 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV622 ) @ SV198 ) @ SV436 ) )
| ( SV436 = SV198 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV622 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7208]) ).
thf(7380,plain,
! [SV199: $i,SV437: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) @ SV199 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) ) )
= $false )
| ( ( SV199
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7209]) ).
thf(7381,plain,
! [SV437: $i,SV199: $i] :
( ( ( SV199
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) @ SV199 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV437 @ tc_HOL_Obool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7210]) ).
thf(7382,plain,
! [SV623: $i,SV438: $i,SV200: $i,SV756: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV756 @ tc_HOL_Obool ) ) @ SV200 ) @ SV438 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV756 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV756 @ tc_HOL_Obool ) ) @ SV623 ) @ SV200 ) ) @ SV438 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV756 @ tc_HOL_Obool ) ) @ SV623 ) @ SV438 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7211]) ).
thf(7383,plain,
! [SV439: $i,SV624: $i,SV201: $i,SV757: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV757 @ SV201 @ SV624 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV757 @ SV201 @ SV439 )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV757 @ SV624 @ SV439 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7212]) ).
thf(7384,plain,
! [SV202: $i,SV440: $i,SV625: $i] :
( ( ( ~ ! [SY2261: $i] : ( hBOOL @ ( hAPP @ SV625 @ SY2261 ) ) )
= $true )
| ( ( ! [SY2262: $i,SY2263: $i] : ( hBOOL @ ( hAPP @ SV625 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV202 ) @ SY2262 ) @ SY2263 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7213]) ).
thf(7385,plain,
! [SV202: $i,SV440: $i,SV625: $i] :
( ( ( ~ ! [SY2264: $i,SY2265: $i] : ( hBOOL @ ( hAPP @ SV625 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV202 ) @ SY2264 ) @ SY2265 ) ) ) )
= $true )
| ( ( ! [SY2266: $i] : ( hBOOL @ ( hAPP @ SV625 @ SY2266 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7214]) ).
thf(7386,plain,
! [SV203: $i,SV441: $i,SV626: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV441 ) @ SV203 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV203 ) @ SV441 ) )
| ( SV203 = SV441 ) )
| ~ ( ( SV203 != SV441 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV203 ) @ SV441 ) ) ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV626 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7215]) ).
thf(7387,plain,
! [SV204: $i,SV442: $i,SV627: $i,SV758: $i,SV829: $i,SV869: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV869 @ ( tc_fun @ SV829 @ tc_HOL_Obool ) ) ) @ SV758 ) @ SV627 ) @ SV442 ) @ SV204 ) ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV758 @ SV442 ) @ SV204 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV627 @ SV442 ) @ SV204 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7216]) ).
thf(7388,plain,
! [SV629: $i,SV207: $i,SV445: $i] :
( ( ( SV445 = SV207 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV629 ) @ SV445 ) @ SV207 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7217]) ).
thf(7389,plain,
! [SV208: $i,SV446: $i,SV630: $i,SV759: $i,SV830: $i,SV870: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV870 @ SV830 ) @ SV759 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV630 @ ( tc_fun @ SV446 @ tc_HOL_Obool ) ) ) @ SV870 ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV208 @ SV830 ) @ SV759 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7218]) ).
thf(7390,plain,
! [SV209: $i,SV447: $i,SV631: $i,SV760: $i,SV831: $i] :
( ( ( c_Finite__Set_Ofun__left__comm__idem @ SV831 @ SV760 @ SV631 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV631 @ SV447 ) @ ( hAPP @ ( hAPP @ SV631 @ SV447 ) @ SV209 ) )
= ( hAPP @ ( hAPP @ SV631 @ SV447 ) @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7219]) ).
thf(7391,plain,
! [SV450: $i,SV212: $i,SV633: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV633 @ tc_HOL_Obool ) ) @ SV212 ) @ SV450 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV633 ) @ SV212 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV633 ) @ SV450 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7220]) ).
thf(7392,plain,
! [SV213: $i,SV451: $i,SV634: $i,SV761: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV761 ) @ SV634 ) @ SV451 ) ) )
= $true )
| ( ( ( SV634 != SV213 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV761 ) @ SV213 ) @ SV451 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV761 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7221]) ).
thf(7393,plain,
! [SV635: $i,SV214: $i,SV452: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV452 ) @ SV214 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV635 ) @ SV214 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV635 ) @ SV452 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7222]) ).
thf(7394,plain,
! [SV762: $i,SV215: $i,SV636: $i,SV453: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV636 ) @ SV215 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV762 ) @ SV215 ) )
= $true )
| ( ( SV762 = SV636 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7223]) ).
thf(7395,plain,
! [SV216: $i,SV454: $i,SV637: $i,SV763: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV763 ) @ SV637 ) @ SV454 ) @ SV216 ) )
| ( SV637 = SV216 )
| ( hBOOL @ ( hAPP @ SV454 @ SV216 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7224]) ).
thf(7396,plain,
! [SV763: $i,SV454: $i,SV216: $i,SV637: $i] :
( ( ~ ( ( SV637 = SV216 )
| ( hBOOL @ ( hAPP @ SV454 @ SV216 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV763 ) @ SV637 ) @ SV454 ) @ SV216 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7225]) ).
thf(7397,plain,
! [SV217: $i,SV455: $i,SV638: $i,SV764: $i,SV832: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
| ~ ! [SY2491: $i] :
~ ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SY2491 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2491 ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SY2491 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2491 ) @ SV217 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7226]) ).
thf(7398,plain,
! [SV217: $i,SV638: $i,SV455: $i,SV832: $i,SV764: $i] :
( ( ~ ( ~ ~ ! [SY2492: $i] :
~ ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SY2492 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2492 ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SY2492 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2492 ) @ SV217 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7226]) ).
thf(7399,plain,
! [SV218: $i,SV456: $i] :
( ( ( class_Finite__Set_Ofinite @ SV456 )
= $false )
| ( ( ~ ( class_Finite__Set_Ofinite @ SV218 ) )
= $true )
| ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV456 @ SV218 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7227]) ).
thf(7400,plain,
! [SV219: $i,SV457: $i,SV639: $i,SV765: $i,SV833: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV833 @ SV765 @ SV639 ) @ SV457 ) @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV639 @ SV219 ) @ SV457 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7228]) ).
thf(7401,plain,
! [SV766: $i,SV221: $i,SV459: $i,SV641: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV641 @ SV459 ) @ SV221 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV641 @ SV221 ) @ SV459 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV766 @ SV641 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7229]) ).
thf(7402,plain,
! [SV642: $i,SV461: $i,SV223: $i,SV767: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV767 ) @ tc_HOL_Obool ) ) @ SV223 ) @ SV461 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV767 @ SV642 @ SV223 )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV767 @ SV642 @ SV461 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7230]) ).
thf(7403,plain,
! [SV224: $i,SV462: $i,SV643: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV643 ) @ SV462 )
!= SV224 )
= $true )
| ( ( SV462
= ( hAPP @ ( c_List_Orev @ SV643 ) @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7231]) ).
thf(7404,plain,
! [SV224: $i,SV643: $i,SV462: $i] :
( ( ( SV462
!= ( hAPP @ ( c_List_Orev @ SV643 ) @ SV224 ) )
= $true )
| ( ( ( hAPP @ ( c_List_Orev @ SV643 ) @ SV462 )
= SV224 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7232]) ).
thf(7405,plain,
! [SV225: $i,SV463: $i,SV644: $i,SV768: $i,SV834: $i] :
( ( ( c_Equiv__Relations_Oequivp @ SV834 @ SV768 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV644 ) @ SV463 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV463 ) @ SV225 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV644 ) @ SV225 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7233]) ).
thf(7406,plain,
! [SV226: $i,SV464: $i,SV645: $i,SV769: $i,SV835: $i,SV871: $i,SV886: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
| ~ ! [SY2430: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SY2430 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2430 ) @ SV226 ) ) ) )
| ~ ( ~ ~ ! [SY2431: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SY2431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2431 ) @ SV226 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7234]) ).
thf(7407,plain,
! [SV227: $i,SV465: $i,SV646: $i,SV770: $i,SV836: $i,SV872: $i,SV887: $i] :
( ( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SV887 @ SV872 @ SV836 @ SV770 @ SV646 @ SV465 )
| ( ( hAPP @ ( hAPP @ SV836 @ SV227 ) @ SV227 )
= SV227 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7235]) ).
thf(7408,plain,
! [SV228: $i,SV466: $i,SV647: $i,SV771: $i,SV837: $i,SV873: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV873 @ SV837 ) @ SV771 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV647 @ ( tc_fun @ SV466 @ tc_HOL_Obool ) ) ) @ SV873 ) @ SV228 ) @ SV837 ) @ SV771 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7236]) ).
thf(7409,plain,
! [SV648: $i,SV229: $i,SV467: $i,SV772: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV772 @ tc_HOL_Obool ) ) @ SV467 ) @ SV229 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV772 ) @ SV648 ) @ SV229 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV772 ) @ SV648 ) @ SV467 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7237]) ).
thf(7410,plain,
! [SV230: $i,SV773: $i,SV468: $i,SV649: $i] :
( ( ( SV649 != SV468 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV773 ) @ SV230 ) @ SV468 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV773 ) @ SV230 ) @ SV649 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV773 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7238]) ).
thf(7411,plain,
! [SV231: $i,SV469: $i,SV650: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV650 ) @ SV469 ) @ SV231 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV650 ) @ SV231 ) @ SV469 ) )
| ( SV231 = SV469 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV650 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7239]) ).
thf(7412,plain,
! [SV233: $i,SV471: $i,SV651: $i,SV774: $i,SV838: $i,SV874: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV874 @ SV838 ) @ SV774 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV651 @ ( tc_fun @ SV471 @ tc_HOL_Obool ) ) ) @ SV233 ) @ SV874 ) @ SV838 ) @ SV774 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7240]) ).
thf(7413,plain,
! [SV775: $i,SV472: $i,SV234: $i,SV652: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV652 @ SV234 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV472 @ SV234 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV775 @ tc_HOL_Obool ) ) @ SV652 ) @ SV472 ) @ SV234 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7241]) ).
thf(7414,plain,
! [SV235: $i,SV473: $i,SV653: $i,SV776: $i,SV839: $i,SV875: $i,SV888: $i] :
( ( ~ ( c_Typedef_Otype__definition @ SV888 @ SV875 @ SV839 @ SV776 @ SV653 )
| ~ ( ~ ( ( ( hAPP @ SV839 @ SV473 )
!= ( hAPP @ SV839 @ SV235 ) )
| ( SV473 = SV235 ) )
| ~ ( ( SV473 != SV235 )
| ( ( hAPP @ SV839 @ SV473 )
= ( hAPP @ SV839 @ SV235 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7242]) ).
thf(7415,plain,
! [SV777: $i,SV474: $i,SV236: $i,SV654: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV654 @ SV236 ) )
| ~ ( hBOOL @ ( hAPP @ SV474 @ SV236 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV777 @ tc_HOL_Obool ) ) @ SV654 ) @ SV474 ) @ SV236 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7243]) ).
thf(7416,plain,
! [SV238: $i,SV476: $i,SV656: $i,SV778: $i,SV840: $i,SV876: $i] :
( ( ( ~ ( c_Typedef_Otype__definition @ SV876 @ SV840 @ SV778 @ SV656 @ SV476 ) )
= $true )
| ( ( ( hAPP @ SV656 @ ( hAPP @ SV778 @ SV238 ) )
= SV238 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7244]) ).
thf(7417,plain,
! [SV239: $i,SV877: $i,SV477: $i] :
( ( ( hBOOL @ ( hAPP @ SV477 @ SV877 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV477 @ ( c_Hilbert__Choice_OEps @ SV239 @ SV477 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7245]) ).
thf(7418,plain,
! [SV479: $i,SV241: $i,SV658: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV658 @ tc_HOL_Obool ) ) @ SV241 ) @ SV479 ) )
= $false )
| ( ( SV479 = SV241 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV658 @ tc_HOL_Obool ) ) @ SV479 ) @ SV241 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7247]) ).
thf(7419,plain,
! [SV480: $i,SV242: $i,SV659: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV659 @ ( tc_fun @ SV659 @ tc_HOL_Obool ) ) ) @ SV242 ) @ SV480 ) )
= $false )
| ( ( c_Wellfounded_OwfP @ SV659 @ SV242 )
= $true )
| ( ( c_Wellfounded_OwfP @ SV659 @ SV480 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7248]) ).
thf(7420,plain,
! [SV660: $i,SV243: $i,SV481: $i] :
( ( ( ~ ( ( SV481 != SV243 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) ) ) ) )
= $false )
| ( ( class_Orderings_Oorder @ SV660 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7249]) ).
thf(7421,plain,
! [SV243: $i,SV481: $i,SV660: $i] :
( ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) ) )
| ( SV481 = SV243 ) ) )
= $false )
| ( ( class_Orderings_Oorder @ SV660 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7249]) ).
thf(7422,plain,
! [SV680: $i,SV65: $i,SV515: $i,SV304: $i] :
( ( ( hBOOL @ ( hAPP @ SV304 @ SV515 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV65 @ tc_HOL_Obool ) ) @ SV680 ) @ SV304 ) @ SV515 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV680 @ SV515 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7252]) ).
thf(7423,plain,
! [SV67: $i,SV306: $i,SV517: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 )
= SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7253]) ).
thf(7424,plain,
! [SV67: $i,SV306: $i,SV517: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 )
= SV67 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV517 @ tc_HOL_Obool ) ) @ SV306 ) @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7254]) ).
thf(7425,plain,
! [SV69: $i,SV308: $i,SV519: $i,SV682: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV682 @ SV519 @ SV308 ) @ SV69 ) ) )
= $true )
| ( ( ~ ! [SY1684: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ SY1684 ) @ SV69 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7255]) ).
thf(7426,plain,
! [SV519: $i,SV682: $i,SV69: $i,SV308: $i] :
( ( ( ~ ~ ! [SY1685: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ SY1685 ) @ SV69 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV682 @ SV519 @ SV308 ) @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7256]) ).
thf(7427,plain,
! [SV309: $i,SV70: $i] :
( ( ( ~ ~ ! [SY1062: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1062 ) @ SY1062 ) )
| ~ ! [SY1063: $i,SY1064: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1064 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1064 ) @ SY1064 ) ) )
| ( ( hAPP @ SV70 @ SY1063 )
!= ( hAPP @ SV70 @ SY1064 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1064 ) @ SY1064 ) ) )
| ( ( hAPP @ SV70 @ SY1063 )
!= ( hAPP @ SV70 @ SY1064 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1064 ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7257]) ).
thf(7428,plain,
! [SV309: $i,SV70: $i] :
( ( ( ~ ~ ! [SY1065: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1065 ) @ SY1065 ) )
| ~ ! [SY1066: $i,SY1067: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7258]) ).
thf(7429,plain,
! [SV520: $i,SV683: $i,SV71: $i,SV310: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV683 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV520 ) ) ) )
= $false )
| ( ( SV683 = SV520 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7259]) ).
thf(7430,plain,
! [SV683: $i,SV520: $i,SV71: $i,SV310: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV520 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV683 ) ) ) )
= $false )
| ( ( SV683 = SV520 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7259]) ).
thf(7431,plain,
! [SV73: $i,SV312: $i,SV521: $i,SV684: $i,SV789: $i,SV848: $i,SV880: $i,SV889: $i] :
( ( ! [SY2536: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2536 @ SV889 @ SV880 @ SV848 ) @ SV789 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV684 @ SV889 @ SV880 @ SV521 ) @ SV312 ) )
| ( ( hAPP @ SV848 @ ( hAPP @ SV789 @ SV73 ) )
= ( hAPP @ SV521 @ ( hAPP @ SV312 @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7260]) ).
thf(7432,plain,
! [SV74: $i,SV313: $i,SV522: $i,SV685: $i] :
( ( ( ! [SY2341: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV685 ) @ ( hAPP @ SV522 @ SY2341 ) ) @ ( hAPP @ SV313 @ SY2341 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV74 @ SV685 ) ) @ SV522 ) @ SV313 ) )
= $true )
| ( ( class_Orderings_Oord @ SV685 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7261]) ).
thf(7433,plain,
! [SV75: $i,SV314: $i,SV523: $i,SV686: $i,SV790: $i,SV849: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV849 @ SV790 ) @ SV686 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV523 @ SV790 ) @ SV686 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV314 @ ( tc_fun @ SV75 @ tc_HOL_Obool ) ) ) @ SV849 ) @ SV523 ) @ SV790 ) @ SV686 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7262]) ).
thf(7434,plain,
! [SV315: $i,SV524: $i,SV77: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV77 @ tc_HOL_Obool ) ) @ SV524 ) @ SV315 ) )
= $true )
| ( ( SV524 = SV315 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7263]) ).
thf(7435,plain,
! [SV524: $i,SV315: $i,SV77: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV77 @ tc_HOL_Obool ) ) @ SV315 ) @ SV524 ) )
= $true )
| ( ( SV524 = SV315 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7264]) ).
thf(7436,plain,
! [SV85: $i,SV323: $i,SV881: $i,SV529: $i] :
( ( ( hBOOL @ ( hAPP @ SV529 @ SV881 ) )
= $false )
| ( ( ( SV323
!= ( c_Hilbert__Choice_OEps @ SV85 @ SV529 ) )
| ( hBOOL @ ( hAPP @ SV529 @ SV323 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7266]) ).
thf(7437,plain,
! [SV530: $i,SV689: $i,SV86: $i,SV324: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) ) ) )
= $true )
| ( ( SV689 = SV530 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7267]) ).
thf(7438,plain,
! [SV531: $i,SV87: $i,SV325: $i,SV690: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV690 @ tc_HOL_Obool ) ) @ SV325 ) @ SV87 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV690 @ tc_HOL_Obool ) ) @ SV531 ) @ SV87 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV690 @ tc_HOL_Obool ) ) @ SV531 ) @ SV325 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7268]) ).
thf(7439,plain,
! [SV88: $i,SV326: $i,SV532: $i,SV691: $i,SV792: $i,SV850: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV850 @ ( tc_fun @ SV792 @ tc_HOL_Obool ) ) ) @ SV691 ) @ SV532 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV691 @ SV326 ) @ SV88 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV532 @ SV326 ) @ SV88 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7269]) ).
thf(7440,plain,
! [SV90: $i,SV328: $i,SV533: $i,SV692: $i,SV793: $i,SV851: $i] :
( ( ( SV851 != SV793 )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV692 @ SV533 @ SV328 @ SV793 @ SV90 ) @ SV851 )
= ( hAPP @ SV328 @ SV851 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7272]) ).
thf(7441,plain,
! [SV91: $i,SV329: $i,SV534: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV534 ) @ SV329 )
= ( hAPP @ ( c_List_Orev @ SV534 ) @ SV91 ) )
= $false )
| ( ( SV329 = SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7273]) ).
thf(7442,plain,
! [SV534: $i,SV91: $i,SV329: $i] :
( ( ( SV329 = SV91 )
= $false )
| ( ( ( hAPP @ ( c_List_Orev @ SV534 ) @ SV329 )
= ( hAPP @ ( c_List_Orev @ SV534 ) @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7274]) ).
thf(7443,plain,
! [SV92: $i,SV330: $i,SV535: $i,SV693: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV693 @ SV535 @ SV330 ) @ SV92 ) ) )
= $true )
| ( ( ~ ! [SY1733: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ SY1733 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7275]) ).
thf(7444,plain,
! [SV535: $i,SV693: $i,SV92: $i,SV330: $i] :
( ( ( ~ ~ ! [SY1734: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ SY1734 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV693 @ SV535 @ SV330 ) @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7276]) ).
thf(7445,plain,
! [SV537: $i,SV694: $i,SV95: $i,SV333: $i,SV794: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ SV333 ) @ SV95 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ SV694 ) @ SV333 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ SV537 ) @ SV95 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ SV694 ) @ SV537 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7277]) ).
thf(7446,plain,
! [SV97: $i,SV335: $i,SV538: $i,SV695: $i,SV795: $i,SV852: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV852 @ ( tc_fun @ SV795 @ tc_HOL_Obool ) ) ) @ SV695 ) @ SV538 ) @ SV335 ) @ SV97 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV695 @ SV335 ) @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7280]) ).
thf(7447,plain,
! [SV99: $i,SV337: $i,SV540: $i,SV696: $i,SV796: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV796 @ SV696 @ SV540 ) @ SV337 ) @ SV99 ) )
| ( hBOOL @ ( hAPP @ SV337 @ ( hAPP @ SV540 @ SV99 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7281]) ).
thf(7448,plain,
! [SV696: $i,SV796: $i,SV99: $i,SV540: $i,SV337: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV337 @ ( hAPP @ SV540 @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV796 @ SV696 @ SV540 ) @ SV337 ) @ SV99 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7282]) ).
thf(7449,plain,
! [SV100: $i,SV338: $i,SV541: $i,SV697: $i,SV797: $i,SV853: $i,SV882: $i,SV890: $i] :
( ( ! [SY2537: $i,SY2538: $i,SY2539: $i] :
( ( ( hAPP @ SY2539 @ ( hAPP @ SY2538 @ SY2537 ) )
!= ( hAPP @ SV890 @ ( hAPP @ SV882 @ SV853 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV797 @ SV697 @ SV541 @ SY2539 ) @ SY2538 ) @ SY2537 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV338 @ SV697 @ SV100 @ SV890 ) @ SV882 ) @ SV853 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7283]) ).
thf(7450,plain,
! [SV101: $i,SV339: $i,SV542: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV339 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) @ SV339 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7284]) ).
thf(7451,plain,
! [SV339: $i,SV101: $i,SV542: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) @ SV339 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV339 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV542 @ tc_HOL_Obool ) ) @ SV101 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7285]) ).
thf(7452,plain,
! [SV102: $i,SV340: $i,SV543: $i,SV698: $i,SV798: $i,SV854: $i] :
( ( ( c_Finite__Set_Ofun__left__comm @ SV854 @ SV798 @ SV698 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV698 @ SV543 ) @ ( hAPP @ ( hAPP @ SV698 @ SV340 ) @ SV102 ) )
= ( hAPP @ ( hAPP @ SV698 @ SV340 ) @ ( hAPP @ ( hAPP @ SV698 @ SV543 ) @ SV102 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7286]) ).
thf(7453,plain,
! [SV103: $i,SV341: $i,SV544: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV103 ) )
= $false )
| ( ( ! [SY2145: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SY2145 ) @ SV103 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SY2145 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7287]) ).
thf(7454,plain,
! [SV544: $i,SV103: $i,SV341: $i] :
( ( ( ! [SY2146: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SY2146 ) @ SV103 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SY2146 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7288]) ).
thf(7455,plain,
! [SV799: $i,SV105: $i,SV343: $i,SV546: $i,SV699: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV546 ) @ SV343 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV343 ) @ SV105 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV546 ) @ SV105 ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV799 @ SV699 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7289]) ).
thf(7456,plain,
! [SV110: $i,SV348: $i,SV548: $i,SV701: $i,SV801: $i] :
( ( ( ( c_Fun_Ofun__upd @ SV801 @ SV701 @ SV548 @ SV348 @ SV110 )
!= SV548 )
| ( ( hAPP @ SV548 @ SV348 )
= SV110 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7292]) ).
thf(7457,plain,
! [SV701: $i,SV801: $i,SV110: $i,SV348: $i,SV548: $i] :
( ( ( ( hAPP @ SV548 @ SV348 )
!= SV110 )
| ( ( c_Fun_Ofun__upd @ SV801 @ SV701 @ SV548 @ SV348 @ SV110 )
= SV548 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7293]) ).
thf(7458,plain,
! [SV112: $i,SV350: $i,SV550: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV112 ) )
= $false )
| ( ( ! [SY2153: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV350 @ SY2153 ) @ SV112 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SY2153 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7294]) ).
thf(7459,plain,
! [SV550: $i,SV112: $i,SV350: $i] :
( ( ( ! [SY2154: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV350 @ SY2154 ) @ SV112 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SY2154 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7295]) ).
thf(7460,plain,
! [SV702: $i,SV113: $i,SV351: $i,SV551: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV551 @ SV351 ) @ SV113 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV551 @ SV113 ) @ SV351 ) )
= $true )
| ( ( c_Predicate_Osymp @ SV702 @ SV551 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7296]) ).
thf(7461,plain,
! [SV114: $i,SV352: $i,SV552: $i,SV703: $i,SV802: $i,SV856: $i] :
( ( ~ ( ( SV856 != SV802 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV703 @ SV552 @ SV352 @ SV802 @ SV114 ) @ SV856 )
= SV114 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7297]) ).
thf(7462,plain,
! [SV114: $i,SV352: $i,SV552: $i,SV703: $i,SV802: $i,SV856: $i] :
( ( ~ ( ~ ( ( SV856 != SV802 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV703 @ SV552 @ SV352 @ SV802 @ SV114 ) @ SV856 )
= ( hAPP @ SV352 @ SV856 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7297]) ).
thf(7463,plain,
! [SV354: $i,SV116: $i] :
( ( ( class_Enum_Oenum @ SV116 )
= $false )
| ( ( class_Enum_Oenum @ SV354 )
= $false )
| ( ( class_Enum_Oenum @ ( tc_fun @ SV354 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7299]) ).
thf(7464,plain,
! [SV117: $i,SV355: $i,SV554: $i,SV704: $i,SV803: $i,SV857: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV704 ) @ SV554 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV355 ) @ SV117 ) )
| ~ ( ( SV704 != SV355 )
| ( SV554 != SV117 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7300]) ).
thf(7465,plain,
! [SV803: $i,SV857: $i,SV117: $i,SV554: $i,SV355: $i,SV704: $i] :
( ( ~ ( ~ ~ ( ( SV704 != SV355 )
| ( SV554 != SV117 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV704 ) @ SV554 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV355 ) @ SV117 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7300]) ).
thf(7466,plain,
! [SV119: $i,SV357: $i,SV555: $i,SV705: $i,SV804: $i,SV858: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV858 @ ( tc_fun @ SV804 @ tc_HOL_Obool ) ) ) @ SV705 ) @ SV555 ) @ SV357 ) @ SV119 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV555 @ SV357 ) @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7301]) ).
thf(7467,plain,
! [SV120: $i,SV358: $i,SV556: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
| ( SV358 = SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7302]) ).
thf(7468,plain,
! [SV120: $i,SV358: $i,SV556: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
| ( SV358 = SV120 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7303]) ).
thf(7469,plain,
! [SV121: $i,SV359: $i,SV706: $i,SV557: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV557 @ SV706 ) ) @ SV359 ) @ SV121 ) )
| ! [SY2373: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV706 ) @ ( hAPP @ SV359 @ SY2373 ) ) @ ( hAPP @ SV121 @ SY2373 ) ) ) ) )
= $false )
| ( ( class_Orderings_Oord @ SV706 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7304]) ).
thf(7470,plain,
! [SV557: $i,SV121: $i,SV359: $i,SV706: $i] :
( ( ( ~ ( ~ ! [SY2374: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV706 ) @ ( hAPP @ SV359 @ SY2374 ) ) @ ( hAPP @ SV121 @ SY2374 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV557 @ SV706 ) ) @ SV359 ) @ SV121 ) ) ) )
= $false )
| ( ( class_Orderings_Oord @ SV706 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7304]) ).
thf(7471,plain,
! [SV123: $i,SV361: $i] :
( ( ( ! [SY1800: $i] :
~ ( hBOOL @ ( hAPP @ SV361 @ SY1800 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV361 @ ( c_Hilbert__Choice_OEps @ SV123 @ SV361 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7305]) ).
thf(7472,plain,
! [SV123: $i,SV361: $i] :
( ( ( ! [SY1801: $i] :
~ ( hBOOL @ ( hAPP @ SV361 @ SY1801 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV361 @ ( c_Hilbert__Choice_OEps @ SV123 @ SV361 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7306]) ).
thf(7473,plain,
! [SV559: $i,SV707: $i,SV363: $i,SV125: $i,SV805: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV805 @ tc_HOL_Obool ) ) @ SV125 ) @ SV363 ) ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV805 @ SV707 @ SV559 @ SV125 )
= $true )
| ( ( c_Fun_Oinj__on @ SV805 @ SV707 @ SV559 @ SV363 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7307]) ).
thf(7474,plain,
! [SV126: $i,SV708: $i,SV364: $i,SV560: $i] :
( ( ( SV560 = SV364 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV708 ) @ SV364 ) @ SV126 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV708 ) @ SV560 ) @ SV126 ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV708 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7308]) ).
thf(7475,plain,
! [SV127: $i,SV365: $i,SV561: $i,SV709: $i,SV806: $i,SV859: $i,SV883: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV883 @ SV859 @ SV806 @ SV709 ) @ SV561 )
!= SV365 )
= $true )
| ( ( ( hAPP @ SV709 @ ( hAPP @ SV561 @ SV127 ) )
= ( hAPP @ SV365 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7309]) ).
thf(7476,plain,
! [SV128: $i,SV366: $i,SV562: $i,SV710: $i,SV807: $i,SV860: $i] :
( ( ~ ( ( SV860 != SV807 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV710 @ SV562 @ SV366 @ SV807 @ SV128 ) @ SV860 )
= SV128 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7310]) ).
thf(7477,plain,
! [SV128: $i,SV366: $i,SV562: $i,SV710: $i,SV807: $i,SV860: $i] :
( ( ~ ( ~ ( ( SV860 != SV807 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV710 @ SV562 @ SV366 @ SV807 @ SV128 ) @ SV860 )
= ( hAPP @ SV366 @ SV860 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7310]) ).
thf(7478,plain,
! [SV129: $i,SV367: $i,SV563: $i,SV711: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV367 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV129 ) )
= $true )
| ( ( SV367 = SV129 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7311]) ).
thf(7479,plain,
! [SV563: $i,SV711: $i,SV129: $i,SV367: $i] :
( ( ( SV367 != SV129 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV367 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7312]) ).
thf(7480,plain,
! [SV130: $i,SV368: $i,SV564: $i,SV712: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV712 ) @ SV564 ) @ SV368 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV712 ) @ SV368 ) @ SV130 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV712 ) @ SV564 ) @ SV130 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV712 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7313]) ).
thf(7481,plain,
! [SV565: $i,SV131: $i,SV713: $i,SV369: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV713 ) @ SV131 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV565 ) @ SV131 ) ) ) )
= $false )
| ( ( SV713 = SV565 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7314]) ).
thf(7482,plain,
! [SV713: $i,SV131: $i,SV565: $i,SV369: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV565 ) @ SV131 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV713 ) @ SV131 ) ) ) )
= $false )
| ( ( SV713 = SV565 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7314]) ).
thf(7483,plain,
! [SV132: $i,SV370: $i,SV566: $i,SV714: $i,SV808: $i,SV861: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV861 ) @ SV808 ) @ SV714 )
= SV566 )
= $false )
| ( ( ( SV370
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV861 ) @ SV714 ) @ SV132 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV861 ) @ SV808 ) @ SV370 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV861 ) @ SV566 ) @ SV132 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7315]) ).
thf(7484,plain,
! [SV133: $i,SV371: $i,SV567: $i,SV715: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV567 ) @ SV371 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV133 ) @ SV371 ) )
= $true )
| ( ( SV567 = SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7316]) ).
thf(7485,plain,
! [SV371: $i,SV715: $i,SV133: $i,SV567: $i] :
( ( ( SV567 != SV133 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV567 ) @ SV371 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV133 ) @ SV371 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7317]) ).
thf(7486,plain,
! [SV716: $i,SV372: $i,SV134: $i,SV568: $i] :
( ( ( hBOOL @ ( hAPP @ SV568 @ SV134 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV372 @ SV134 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV716 @ tc_HOL_Obool ) ) @ SV568 ) @ SV372 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7318]) ).
thf(7487,plain,
! [SV717: $i,SV135: $i,SV373: $i,SV569: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV569 @ SV373 ) @ SV135 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV569 @ SV135 ) @ SV373 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV717 @ SV569 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7319]) ).
thf(7488,plain,
! [SV374: $i,SV136: $i,SV570: $i,SV718: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV718 @ SV570 ) @ SV136 ) )
= $false )
| ( ( SV374 = SV136 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV718 @ SV570 ) @ SV374 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7320]) ).
thf(7489,plain,
! [SV137: $i,SV375: $i,SV571: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV571 ) @ SV375 ) @ SV137 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV137 @ SV375 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7321]) ).
thf(7490,plain,
! [SV571: $i,SV375: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ SV137 @ SV375 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV571 ) @ SV375 ) @ SV137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7322]) ).
thf(7491,plain,
! [SV142: $i,SV380: $i,SV575: $i,SV720: $i,SV810: $i,SV862: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV862 @ ( tc_fun @ SV810 @ tc_HOL_Obool ) ) ) @ SV720 ) @ SV575 ) @ SV380 ) @ SV142 ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV720 @ SV380 ) @ SV142 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV575 @ SV380 ) @ SV142 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7326]) ).
thf(7492,plain,
! [SV381: $i,SV143: $i,SV576: $i,SV721: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV576 ) @ SV143 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV576 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV381 ) @ SV143 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV576 ) @ SV381 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7327]) ).
thf(7493,plain,
! [SV144: $i,SV382: $i,SV577: $i] :
( ( ( SV577 = SV382 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV577 ) @ SV382 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV382 ) @ SV577 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7328]) ).
thf(7494,plain,
! [SV382: $i,SV577: $i,SV144: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV577 ) @ SV382 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV382 ) @ SV577 ) ) ) )
= $false )
| ( ( SV577 = SV382 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7329]) ).
thf(7495,plain,
! [SV579: $i,SV146: $i,SV722: $i,SV384: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV384 @ tc_HOL_Obool ) ) @ SV722 ) @ SV146 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV146 @ SV579 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV722 @ SV579 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7330]) ).
thf(7496,plain,
! [SV580: $i,SV147: $i,SV385: $i,SV723: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV723 @ tc_HOL_Obool ) ) @ SV385 ) @ SV147 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV723 @ tc_HOL_Obool ) ) @ SV580 ) @ SV147 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV723 @ tc_HOL_Obool ) ) @ SV580 ) @ SV385 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7331]) ).
thf(7497,plain,
! [SV150: $i,SV388: $i,SV583: $i,SV811: $i,SV725: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV725 @ SV811 ) ) @ SV583 ) @ SV388 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV811 ) @ ( hAPP @ SV583 @ SV150 ) ) @ ( hAPP @ SV388 @ SV150 ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV811 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7333]) ).
thf(7498,plain,
! [SV152: $i,SV390: $i,SV585: $i,SV727: $i,SV813: $i,SV863: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV863 @ SV813 ) @ SV727 ) @ SV585 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV863 @ SV813 ) @ SV390 ) @ SV152 ) )
= $false )
| ( ( ~ ( ( SV727 != SV390 )
| ( SV585 != SV152 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7335]) ).
thf(7499,plain,
! [SV391: $i,SV586: $i,SV153: $i,SV728: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV728 ) @ SV153 ) @ SV586 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV728 ) @ SV153 ) @ SV391 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV728 @ tc_HOL_Obool ) ) @ SV586 ) @ SV391 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7336]) ).
thf(7500,plain,
! [SV392: $i,SV587: $i,SV154: $i,SV729: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV729 ) @ SV154 ) @ SV587 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV729 ) @ SV154 ) @ SV392 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV729 @ tc_HOL_Obool ) ) @ SV587 ) @ SV392 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7337]) ).
thf(7501,plain,
! [SV155: $i,SV393: $i,SV588: $i,SV730: $i,SV814: $i,SV864: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV864 @ SV814 ) @ SV730 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV588 @ SV814 ) @ SV730 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV393 @ ( tc_fun @ SV155 @ tc_HOL_Obool ) ) ) @ SV588 ) @ SV864 ) @ SV814 ) @ SV730 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7338]) ).
thf(7502,plain,
! [SV156: $i,SV394: $i,SV589: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
| ~ ( ( SV394 != SV156 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7339]) ).
thf(7503,plain,
! [SV156: $i,SV394: $i,SV589: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
| ~ ( ( SV394 != SV156 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7340]) ).
thf(7504,plain,
! [SV159: $i,SV397: $i,SV591: $i,SV732: $i,SV815: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV815 @ SV732 @ SV591 ) @ SV397 ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV591 @ SV159 ) @ SV397 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7341]) ).
thf(7505,plain,
! [SV732: $i,SV815: $i,SV397: $i,SV159: $i,SV591: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV591 @ SV159 ) @ SV397 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV815 @ SV732 @ SV591 ) @ SV397 ) @ SV159 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7342]) ).
thf(7506,plain,
! [SV816: $i,SV160: $i,SV398: $i,SV592: $i,SV733: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV592 ) @ SV398 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV398 ) @ SV160 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV592 ) @ SV160 ) ) )
= $true )
| ( ( c_Predicate_Otransp @ SV816 @ SV733 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7343]) ).
thf(7507,plain,
! [SV161: $i,SV399: $i,SV593: $i] :
( ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV399 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV161 ) )
= $false )
| ( ( SV399 = SV161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7344]) ).
thf(7508,plain,
! [SV593: $i,SV161: $i,SV399: $i] :
( ( ( SV399 = SV161 )
= $false )
| ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV399 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV593 @ tc_HOL_Obool ) ) @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7345]) ).
thf(7509,plain,
! [SV162: $i,SV400: $i,SV594: $i,SV817: $i,SV734: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV734 @ SV817 ) ) @ SV594 ) @ SV400 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV817 ) @ ( hAPP @ SV594 @ SV162 ) ) @ ( hAPP @ SV400 @ SV162 ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV817 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7346]) ).
thf(7510,plain,
! [SV163: $i,SV401: $i,SV595: $i,SV735: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV735 ) @ SV595 ) @ SV401 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV735 ) @ SV163 ) @ SV595 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV735 ) @ SV163 ) @ SV401 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV735 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7347]) ).
thf(7511,plain,
! [SV736: $i,SV403: $i,SV165: $i,SV596: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV596 @ SV165 ) @ SV403 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV736 @ SV596 ) @ SV165 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV736 @ SV596 ) @ SV403 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7350]) ).
thf(7512,plain,
! [SV166: $i,SV404: $i,SV597: $i,SV737: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV737 ) @ SV597 ) @ SV404 ) )
= $false )
| ( ( ( SV404 != SV166 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV737 ) @ SV597 ) @ SV166 ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV737 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7351]) ).
thf(7513,plain,
! [SV169: $i,SV407: $i,SV600: $i,SV739: $i,SV818: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
| ~ ! [SY2478: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SY2478 ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SY2478 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7352]) ).
thf(7514,plain,
! [SV407: $i,SV818: $i,SV739: $i,SV169: $i,SV600: $i] :
( ( ~ ~ ! [SY2479: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SY2479 ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SY2479 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7353]) ).
thf(7515,plain,
! [SV170: $i,SV408: $i,SV601: $i,SV740: $i,SV819: $i,SV865: $i] :
( ( ( SV865 = SV819 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV740 @ SV601 @ SV408 ) @ SV170 ) @ SV865 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV740 @ SV601 @ SV408 ) @ SV170 ) @ SV819 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7354]) ).
thf(7516,plain,
! [SV409: $i,SV171: $i,SV602: $i,SV741: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV741 @ SV602 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV171 @ tc_HOL_Obool ) ) @ SV409 ) @ SV741 ) @ SV602 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7355]) ).
thf(7517,plain,
! [SV603: $i,SV172: $i,SV410: $i,SV742: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV742 @ tc_HOL_Obool ) ) @ SV410 ) @ SV172 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV742 @ tc_HOL_Obool ) ) @ SV410 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV742 @ tc_HOL_Obool ) ) @ SV172 ) @ SV603 ) )
= SV603 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV742 @ tc_HOL_Obool ) ) @ SV603 ) @ SV410 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7357]) ).
thf(7518,plain,
! [SV173: $i,SV411: $i,SV604: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV604 ) @ SV411 ) @ SV173 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV604 ) @ SV173 ) @ SV411 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV604 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7358]) ).
thf(7519,plain,
! [SV415: $i,SV606: $i,SV177: $i,SV744: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV744 ) @ SV177 ) @ SV606 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV744 ) @ SV177 ) @ SV415 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV744 @ tc_HOL_Obool ) ) @ SV606 ) @ SV415 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7359]) ).
thf(7520,plain,
! [SV607: $i,SV745: $i,SV178: $i,SV416: $i,SV820: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV416 ) @ SV178 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV745 ) @ SV416 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV607 ) @ SV178 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV745 ) @ SV607 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7360]) ).
thf(7521,plain,
! [SV179: $i,SV417: $i,SV608: $i,SV746: $i,SV821: $i,SV866: $i] :
( ( ( SV866 != SV821 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ SV608 ) @ SV866 ) @ SV417 ) ) @ SV821 ) @ SV179 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ SV608 ) @ SV821 ) @ SV179 ) ) @ SV866 ) @ SV417 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7361]) ).
thf(7522,plain,
! [SV181: $i,SV419: $i,SV610: $i,SV748: $i,SV823: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV823 @ SV748 @ SV610 ) @ SV419 ) @ SV181 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV610 @ SV181 ) @ SV419 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7363]) ).
thf(7523,plain,
! [SV748: $i,SV823: $i,SV419: $i,SV181: $i,SV610: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV610 @ SV181 ) @ SV419 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV823 @ SV748 @ SV610 ) @ SV419 ) @ SV181 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7364]) ).
thf(7524,plain,
! [SV183: $i,SV421: $i,SV611: $i,SV749: $i,SV824: $i,SV867: $i,SV884: $i,SV891: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV891 @ SV884 @ SV867 @ SV824 ) @ SV749 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV611 @ SV884 @ SV867 @ SV421 ) @ SV183 ) )
| ! [SY2485: $i] :
( ( hAPP @ SV824 @ ( hAPP @ SV749 @ SY2485 ) )
= ( hAPP @ SV421 @ ( hAPP @ SV183 @ SY2485 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7367]) ).
thf(7525,plain,
! [SV422: $i,SV892: $i,SV184: $i] :
( ( ( ! [SY2541: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SV892 ) @ SY2541 ) )
| ( ( hAPP @ SV184 @ SV892 )
= ( hAPP @ SV184 @ SY2541 ) ) )
| ~ ( ( ( hAPP @ SV184 @ SV892 )
!= ( hAPP @ SV184 @ SY2541 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SV892 ) @ SY2541 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[7368]) ).
thf(7526,plain,
! [SV422: $i,SV184: $i] :
( ( ( ! [SY2542: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ SY2542 ) )
| ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
= ( hAPP @ SV184 @ SY2542 ) ) )
| ~ ( ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
!= ( hAPP @ SV184 @ SY2542 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ SY2542 ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[7369]) ).
thf(7527,plain,
! [SV186: $i,SV424: $i,SV613: $i,SV751: $i,SV826: $i,SV868: $i,SV885: $i,SV893: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV893 @ SV885 ) @ SV868 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV826 @ SV868 ) @ SV751 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV613 @ SV424 @ SV186 @ SV893 @ SV826 ) @ SV885 ) @ SV751 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7371]) ).
thf(7528,plain,
! [SV187: $i,SV425: $i,SV614: $i,SV752: $i,SV827: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV752 ) @ SV614 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV425 ) @ SV187 ) )
| ~ ( ( SV752 != SV425 )
| ( SV614 != SV187 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7372]) ).
thf(7529,plain,
! [SV827: $i,SV187: $i,SV614: $i,SV425: $i,SV752: $i] :
( ( ~ ~ ( ( SV752 != SV425 )
| ( SV614 != SV187 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV752 ) @ SV614 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV425 ) @ SV187 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7373]) ).
thf(7530,plain,
! [SV616: $i,SV191: $i,SV429: $i,SV753: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SV429 ) @ SV191 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SV616 ) @ SV191 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SV616 ) @ SV429 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7374]) ).
thf(7531,plain,
! [SV617: $i,SV754: $i,SV192: $i,SV430: $i,SV828: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ SV430 ) @ SV192 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ SV754 ) @ SV192 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ SV617 ) @ SV430 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ SV754 ) @ SV617 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7375]) ).
thf(7532,plain,
! [SV620: $i,SV196: $i,SV434: $i,SV755: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV755 @ tc_HOL_Obool ) ) @ SV434 ) @ SV196 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV755 @ tc_HOL_Obool ) ) @ SV620 ) @ SV196 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV755 @ tc_HOL_Obool ) ) @ SV620 ) @ SV434 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7376]) ).
thf(7533,plain,
! [SV197: $i,SV435: $i,SV621: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV621 @ SV435 ) @ SV197 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV435 @ SV197 ) @ SV197 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7377]) ).
thf(7534,plain,
! [SV621: $i,SV197: $i,SV435: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV435 @ SV197 ) @ SV197 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV621 @ SV435 ) @ SV197 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7378]) ).
thf(7535,plain,
! [SV436: $i,SV198: $i,SV622: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV622 ) @ SV198 ) @ SV436 ) ) )
= $true )
| ( ( SV436 = SV198 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV622 ) @ SV436 ) @ SV198 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV622 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7379]) ).
thf(7536,plain,
! [SV623: $i,SV438: $i,SV200: $i,SV756: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV756 @ tc_HOL_Obool ) ) @ SV200 ) @ SV438 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV756 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV756 @ tc_HOL_Obool ) ) @ SV623 ) @ SV200 ) ) @ SV438 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV756 @ tc_HOL_Obool ) ) @ SV623 ) @ SV438 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7382]) ).
thf(7537,plain,
! [SV439: $i,SV624: $i,SV201: $i,SV757: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV757 @ SV201 @ SV624 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV757 @ SV201 @ SV439 )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV757 @ SV624 @ SV439 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7383]) ).
thf(7538,plain,
! [SV202: $i,SV440: $i,SV625: $i] :
( ( ( ! [SY2261: $i] : ( hBOOL @ ( hAPP @ SV625 @ SY2261 ) ) )
= $false )
| ( ( ! [SY2262: $i,SY2263: $i] : ( hBOOL @ ( hAPP @ SV625 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV202 ) @ SY2262 ) @ SY2263 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7384]) ).
thf(7539,plain,
! [SV202: $i,SV440: $i,SV625: $i] :
( ( ( ! [SY2264: $i,SY2265: $i] : ( hBOOL @ ( hAPP @ SV625 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV202 ) @ SY2264 ) @ SY2265 ) ) ) )
= $false )
| ( ( ! [SY2266: $i] : ( hBOOL @ ( hAPP @ SV625 @ SY2266 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7385]) ).
thf(7540,plain,
! [SV441: $i,SV203: $i,SV626: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV203 ) @ SV441 ) )
| ( SV203 = SV441 ) )
| ~ ( ( SV203 != SV441 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV203 ) @ SV441 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV441 ) @ SV203 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV626 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7386]) ).
thf(7541,plain,
! [SV204: $i,SV442: $i,SV627: $i,SV758: $i,SV829: $i,SV869: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV869 @ ( tc_fun @ SV829 @ tc_HOL_Obool ) ) ) @ SV758 ) @ SV627 ) @ SV442 ) @ SV204 ) )
= $false )
| ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV758 @ SV442 ) @ SV204 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV627 @ SV442 ) @ SV204 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7387]) ).
thf(7542,plain,
! [SV208: $i,SV446: $i,SV630: $i,SV759: $i,SV830: $i,SV870: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV870 @ SV830 ) @ SV759 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV630 @ ( tc_fun @ SV446 @ tc_HOL_Obool ) ) ) @ SV870 ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV208 @ SV830 ) @ SV759 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7389]) ).
thf(7543,plain,
! [SV213: $i,SV451: $i,SV634: $i,SV761: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV761 ) @ SV634 ) @ SV451 ) )
= $false )
| ( ( ( SV634 != SV213 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV761 ) @ SV213 ) @ SV451 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV761 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7392]) ).
thf(7544,plain,
! [SV762: $i,SV215: $i,SV636: $i,SV453: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV636 ) @ SV215 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV762 ) @ SV215 ) )
= $true )
| ( ( SV762 = SV636 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7394]) ).
thf(7545,plain,
! [SV216: $i,SV454: $i,SV637: $i,SV763: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV763 ) @ SV637 ) @ SV454 ) @ SV216 ) ) )
= $true )
| ( ( ( SV637 = SV216 )
| ( hBOOL @ ( hAPP @ SV454 @ SV216 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7395]) ).
thf(7546,plain,
! [SV763: $i,SV454: $i,SV216: $i,SV637: $i] :
( ( ( ~ ( ( SV637 = SV216 )
| ( hBOOL @ ( hAPP @ SV454 @ SV216 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV763 ) @ SV637 ) @ SV454 ) @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7396]) ).
thf(7547,plain,
! [SV217: $i,SV455: $i,SV638: $i,SV764: $i,SV832: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
| ~ ! [SY2491: $i] :
~ ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SY2491 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2491 ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SY2491 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2491 ) @ SV217 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7397]) ).
thf(7548,plain,
! [SV217: $i,SV638: $i,SV455: $i,SV832: $i,SV764: $i] :
( ( ~ ~ ! [SY2492: $i] :
~ ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SY2492 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2492 ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SY2492 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2492 ) @ SV217 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7398]) ).
thf(7549,plain,
! [SV456: $i,SV218: $i] :
( ( ( class_Finite__Set_Ofinite @ SV218 )
= $false )
| ( ( class_Finite__Set_Ofinite @ SV456 )
= $false )
| ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV456 @ SV218 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7399]) ).
thf(7550,plain,
! [SV766: $i,SV221: $i,SV459: $i,SV641: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV641 @ SV459 ) @ SV221 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV641 @ SV221 ) @ SV459 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV766 @ SV641 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7401]) ).
thf(7551,plain,
! [SV642: $i,SV461: $i,SV223: $i,SV767: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV767 ) @ tc_HOL_Obool ) ) @ SV223 ) @ SV461 ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV767 @ SV642 @ SV223 )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV767 @ SV642 @ SV461 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7402]) ).
thf(7552,plain,
! [SV224: $i,SV462: $i,SV643: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV643 ) @ SV462 )
= SV224 )
= $false )
| ( ( SV462
= ( hAPP @ ( c_List_Orev @ SV643 ) @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7403]) ).
thf(7553,plain,
! [SV224: $i,SV643: $i,SV462: $i] :
( ( ( SV462
= ( hAPP @ ( c_List_Orev @ SV643 ) @ SV224 ) )
= $false )
| ( ( ( hAPP @ ( c_List_Orev @ SV643 ) @ SV462 )
= SV224 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7404]) ).
thf(7554,plain,
! [SV834: $i,SV225: $i,SV463: $i,SV644: $i,SV768: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV644 ) @ SV463 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV463 ) @ SV225 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV644 ) @ SV225 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV834 @ SV768 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7405]) ).
thf(7555,plain,
! [SV226: $i,SV464: $i,SV645: $i,SV769: $i,SV835: $i,SV871: $i,SV886: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
| ~ ! [SY2430: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SY2430 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2430 ) @ SV226 ) ) ) )
| ~ ( ~ ~ ! [SY2431: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SY2431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2431 ) @ SV226 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7406]) ).
thf(7556,plain,
! [SV227: $i,SV465: $i,SV646: $i,SV770: $i,SV836: $i,SV872: $i,SV887: $i] :
( ( ( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SV887 @ SV872 @ SV836 @ SV770 @ SV646 @ SV465 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV836 @ SV227 ) @ SV227 )
= SV227 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7407]) ).
thf(7557,plain,
! [SV228: $i,SV466: $i,SV647: $i,SV771: $i,SV837: $i,SV873: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV873 @ SV837 ) @ SV771 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV647 @ ( tc_fun @ SV466 @ tc_HOL_Obool ) ) ) @ SV873 ) @ SV228 ) @ SV837 ) @ SV771 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7408]) ).
thf(7558,plain,
! [SV648: $i,SV229: $i,SV467: $i,SV772: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV772 @ tc_HOL_Obool ) ) @ SV467 ) @ SV229 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV772 ) @ SV648 ) @ SV229 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV772 ) @ SV648 ) @ SV467 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7409]) ).
thf(7559,plain,
! [SV230: $i,SV773: $i,SV468: $i,SV649: $i] :
( ( ( SV649 = SV468 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV773 ) @ SV230 ) @ SV468 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV773 ) @ SV230 ) @ SV649 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV773 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7410]) ).
thf(7560,plain,
! [SV469: $i,SV231: $i,SV650: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV650 ) @ SV231 ) @ SV469 ) ) )
= $true )
| ( ( SV231 = SV469 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV650 ) @ SV469 ) @ SV231 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV650 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7411]) ).
thf(7561,plain,
! [SV233: $i,SV471: $i,SV651: $i,SV774: $i,SV838: $i,SV874: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV874 @ SV838 ) @ SV774 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV651 @ ( tc_fun @ SV471 @ tc_HOL_Obool ) ) ) @ SV233 ) @ SV874 ) @ SV838 ) @ SV774 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7412]) ).
thf(7562,plain,
! [SV775: $i,SV472: $i,SV234: $i,SV652: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV652 @ SV234 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV472 @ SV234 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV775 @ tc_HOL_Obool ) ) @ SV652 ) @ SV472 ) @ SV234 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7413]) ).
thf(7563,plain,
! [SV235: $i,SV473: $i,SV653: $i,SV776: $i,SV839: $i,SV875: $i,SV888: $i] :
( ( ( ~ ( c_Typedef_Otype__definition @ SV888 @ SV875 @ SV839 @ SV776 @ SV653 ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP @ SV839 @ SV473 )
!= ( hAPP @ SV839 @ SV235 ) )
| ( SV473 = SV235 ) )
| ~ ( ( SV473 != SV235 )
| ( ( hAPP @ SV839 @ SV473 )
= ( hAPP @ SV839 @ SV235 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7414]) ).
thf(7564,plain,
! [SV474: $i,SV777: $i,SV236: $i,SV654: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV654 @ SV236 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV777 @ tc_HOL_Obool ) ) @ SV654 ) @ SV474 ) @ SV236 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7415]) ).
thf(7565,plain,
! [SV654: $i,SV777: $i,SV236: $i,SV474: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV474 @ SV236 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV777 @ tc_HOL_Obool ) ) @ SV654 ) @ SV474 ) @ SV236 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7415]) ).
thf(7566,plain,
! [SV238: $i,SV476: $i,SV656: $i,SV778: $i,SV840: $i,SV876: $i] :
( ( ( c_Typedef_Otype__definition @ SV876 @ SV840 @ SV778 @ SV656 @ SV476 )
= $false )
| ( ( ( hAPP @ SV656 @ ( hAPP @ SV778 @ SV238 ) )
= SV238 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7416]) ).
thf(7567,plain,
! [SV660: $i,SV243: $i,SV481: $i] :
( ( ( ( SV481 != SV243 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV660 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7420]) ).
thf(7568,plain,
! [SV243: $i,SV481: $i,SV660: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) ) )
| ( SV481 = SV243 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV660 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7421]) ).
thf(7569,plain,
! [SV69: $i,SV308: $i,SV519: $i,SV682: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV682 @ SV519 @ SV308 ) @ SV69 ) )
= $false )
| ( ( ~ ! [SY1684: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ SY1684 ) @ SV69 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7425]) ).
thf(7570,plain,
! [SV519: $i,SV682: $i,SV69: $i,SV308: $i] :
( ( ( ~ ! [SY1685: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ SY1685 ) @ SV69 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV682 @ SV519 @ SV308 ) @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7426]) ).
thf(7571,plain,
! [SV309: $i,SV70: $i] :
( ( ( ~ ~ ! [SY1062: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1062 ) @ SY1062 ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7427]) ).
thf(7572,plain,
! [SV309: $i,SV70: $i] :
( ( ( ~ ! [SY1063: $i,SY1064: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1064 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1064 ) @ SY1064 ) ) )
| ( ( hAPP @ SV70 @ SY1063 )
!= ( hAPP @ SV70 @ SY1064 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1064 ) @ SY1064 ) ) )
| ( ( hAPP @ SV70 @ SY1063 )
!= ( hAPP @ SV70 @ SY1064 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1064 ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7427]) ).
thf(7573,plain,
! [SV309: $i,SV70: $i] :
( ( ( ~ ~ ! [SY1065: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1065 ) @ SY1065 ) ) )
= $true )
| ( ( ~ ! [SY1066: $i,SY1067: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7428]) ).
thf(7574,plain,
! [SV520: $i,SV683: $i,SV71: $i,SV310: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV683 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV520 ) ) )
= $true )
| ( ( SV683 = SV520 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7429]) ).
thf(7575,plain,
! [SV683: $i,SV520: $i,SV71: $i,SV310: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV520 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV683 ) ) )
= $true )
| ( ( SV683 = SV520 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7430]) ).
thf(7576,plain,
! [SV73: $i,SV312: $i,SV521: $i,SV684: $i,SV789: $i,SV848: $i,SV880: $i,SV889: $i,SV894: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV894 @ SV889 @ SV880 @ SV848 ) @ SV789 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV684 @ SV889 @ SV880 @ SV521 ) @ SV312 ) )
| ( ( hAPP @ SV848 @ ( hAPP @ SV789 @ SV73 ) )
= ( hAPP @ SV521 @ ( hAPP @ SV312 @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7431]) ).
thf(7577,plain,
! [SV313: $i,SV74: $i,SV522: $i,SV685: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV685 ) @ ( hAPP @ SV522 @ ( sK4_SY2341 @ SV74 @ SV313 @ SV522 @ SV685 ) ) ) @ ( hAPP @ SV313 @ ( sK4_SY2341 @ SV74 @ SV313 @ SV522 @ SV685 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV74 @ SV685 ) ) @ SV522 ) @ SV313 ) )
= $true )
| ( ( class_Orderings_Oord @ SV685 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[7432]) ).
thf(7578,plain,
! [SV849: $i,SV75: $i,SV314: $i,SV686: $i,SV790: $i,SV523: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV523 @ SV790 ) @ SV686 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV314 @ ( tc_fun @ SV75 @ tc_HOL_Obool ) ) ) @ SV849 ) @ SV523 ) @ SV790 ) @ SV686 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV849 @ SV790 ) @ SV686 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7433]) ).
thf(7579,plain,
! [SV881: $i,SV529: $i,SV85: $i,SV323: $i] :
( ( ( SV323
!= ( c_Hilbert__Choice_OEps @ SV85 @ SV529 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV529 @ SV323 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV529 @ SV881 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7436]) ).
thf(7580,plain,
! [SV530: $i,SV689: $i,SV86: $i,SV324: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) ) ) )
= $true )
| ( ( SV689 = SV530 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7437]) ).
thf(7581,plain,
! [SV689: $i,SV530: $i,SV86: $i,SV324: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) ) ) )
= $true )
| ( ( SV689 = SV530 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7437]) ).
thf(7582,plain,
! [SV792: $i,SV850: $i,SV532: $i,SV88: $i,SV326: $i,SV691: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV691 @ SV326 ) @ SV88 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV532 @ SV326 ) @ SV88 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV850 @ ( tc_fun @ SV792 @ tc_HOL_Obool ) ) ) @ SV691 ) @ SV532 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7439]) ).
thf(7583,plain,
! [SV90: $i,SV328: $i,SV533: $i,SV692: $i,SV793: $i,SV851: $i] :
( ( ( SV851 = SV793 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV692 @ SV533 @ SV328 @ SV793 @ SV90 ) @ SV851 )
= ( hAPP @ SV328 @ SV851 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7440]) ).
thf(7584,plain,
! [SV92: $i,SV330: $i,SV535: $i,SV693: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV693 @ SV535 @ SV330 ) @ SV92 ) )
= $false )
| ( ( ~ ! [SY1733: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ SY1733 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7443]) ).
thf(7585,plain,
! [SV535: $i,SV693: $i,SV92: $i,SV330: $i] :
( ( ( ~ ! [SY1734: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ SY1734 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV693 @ SV535 @ SV330 ) @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7444]) ).
thf(7586,plain,
! [SV537: $i,SV694: $i,SV95: $i,SV333: $i,SV794: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ SV333 ) @ SV95 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ SV694 ) @ SV333 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ SV537 ) @ SV95 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) @ SV694 ) @ SV537 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7445]) ).
thf(7587,plain,
! [SV99: $i,SV337: $i,SV540: $i,SV696: $i,SV796: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV796 @ SV696 @ SV540 ) @ SV337 ) @ SV99 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV337 @ ( hAPP @ SV540 @ SV99 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7447]) ).
thf(7588,plain,
! [SV696: $i,SV796: $i,SV99: $i,SV540: $i,SV337: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV337 @ ( hAPP @ SV540 @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV796 @ SV696 @ SV540 ) @ SV337 ) @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7448]) ).
thf(7589,plain,
! [SV100: $i,SV338: $i,SV541: $i,SV697: $i,SV797: $i,SV853: $i,SV882: $i,SV890: $i,SV895: $i] :
( ( ! [SY2543: $i,SY2544: $i] :
( ( ( hAPP @ SY2544 @ ( hAPP @ SY2543 @ SV895 ) )
!= ( hAPP @ SV890 @ ( hAPP @ SV882 @ SV853 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV797 @ SV697 @ SV541 @ SY2544 ) @ SY2543 ) @ SV895 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV338 @ SV697 @ SV100 @ SV890 ) @ SV882 ) @ SV853 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7449]) ).
thf(7590,plain,
! [SV544: $i,SV103: $i,SV896: $i,SV341: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV896 ) @ SV103 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV896 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV103 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[7453]) ).
thf(7591,plain,
! [SV103: $i,SV544: $i,SV341: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ ( sK5_SY2146 @ SV544 @ SV103 @ SV341 ) ) @ SV103 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ ( sK5_SY2146 @ SV544 @ SV103 @ SV341 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV103 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[7454]) ).
thf(7592,plain,
! [SV799: $i,SV105: $i,SV343: $i,SV546: $i,SV699: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV546 ) @ SV343 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV343 ) @ SV105 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV546 ) @ SV105 ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV799 @ SV699 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7455]) ).
thf(7593,plain,
! [SV110: $i,SV348: $i,SV548: $i,SV701: $i,SV801: $i] :
( ( ( ( c_Fun_Ofun__upd @ SV801 @ SV701 @ SV548 @ SV348 @ SV110 )
!= SV548 )
= $true )
| ( ( ( hAPP @ SV548 @ SV348 )
= SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7456]) ).
thf(7594,plain,
! [SV701: $i,SV801: $i,SV110: $i,SV348: $i,SV548: $i] :
( ( ( ( hAPP @ SV548 @ SV348 )
!= SV110 )
= $true )
| ( ( ( c_Fun_Ofun__upd @ SV801 @ SV701 @ SV548 @ SV348 @ SV110 )
= SV548 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7457]) ).
thf(7595,plain,
! [SV550: $i,SV112: $i,SV897: $i,SV350: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV350 @ SV897 ) @ SV112 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV897 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV112 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[7458]) ).
thf(7596,plain,
! [SV112: $i,SV550: $i,SV350: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV350 @ ( sK6_SY2154 @ SV550 @ SV112 @ SV350 ) ) @ SV112 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ ( sK6_SY2154 @ SV550 @ SV112 @ SV350 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV112 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[7459]) ).
thf(7597,plain,
! [SV114: $i,SV352: $i,SV552: $i,SV703: $i,SV802: $i,SV856: $i] :
( ( ( SV856 != SV802 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV703 @ SV552 @ SV352 @ SV802 @ SV114 ) @ SV856 )
= SV114 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7461]) ).
thf(7598,plain,
! [SV114: $i,SV352: $i,SV552: $i,SV703: $i,SV802: $i,SV856: $i] :
( ( ~ ( ( SV856 != SV802 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV703 @ SV552 @ SV352 @ SV802 @ SV114 ) @ SV856 )
= ( hAPP @ SV352 @ SV856 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7462]) ).
thf(7599,plain,
! [SV117: $i,SV355: $i,SV554: $i,SV704: $i,SV803: $i,SV857: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV704 ) @ SV554 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV355 ) @ SV117 ) )
| ~ ( ( SV704 != SV355 )
| ( SV554 != SV117 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7464]) ).
thf(7600,plain,
! [SV803: $i,SV857: $i,SV117: $i,SV554: $i,SV355: $i,SV704: $i] :
( ( ~ ~ ( ( SV704 != SV355 )
| ( SV554 != SV117 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV704 ) @ SV554 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV355 ) @ SV117 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7465]) ).
thf(7601,plain,
! [SV120: $i,SV358: $i,SV556: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
= $true )
| ( ( SV358 = SV120 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7467]) ).
thf(7602,plain,
! [SV120: $i,SV358: $i,SV556: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7468]) ).
thf(7603,plain,
! [SV556: $i,SV120: $i,SV358: $i] :
( ( ( SV358 = SV120 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV556 @ tc_HOL_Obool ) ) @ SV358 ) @ SV120 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7468]) ).
thf(7604,plain,
! [SV121: $i,SV359: $i,SV706: $i,SV557: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV557 @ SV706 ) ) @ SV359 ) @ SV121 ) )
| ! [SY2373: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV706 ) @ ( hAPP @ SV359 @ SY2373 ) ) @ ( hAPP @ SV121 @ SY2373 ) ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV706 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7469]) ).
thf(7605,plain,
! [SV557: $i,SV121: $i,SV359: $i,SV706: $i] :
( ( ( ~ ! [SY2374: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV706 ) @ ( hAPP @ SV359 @ SY2374 ) ) @ ( hAPP @ SV121 @ SY2374 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV557 @ SV706 ) ) @ SV359 ) @ SV121 ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV706 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7470]) ).
thf(7606,plain,
! [SV123: $i,SV361: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV361 @ ( sK7_SY1800 @ SV123 @ SV361 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV361 @ ( c_Hilbert__Choice_OEps @ SV123 @ SV361 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[7471]) ).
thf(7607,plain,
! [SV123: $i,SV898: $i,SV361: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV361 @ SV898 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV361 @ ( c_Hilbert__Choice_OEps @ SV123 @ SV361 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[7472]) ).
thf(7608,plain,
! [SV559: $i,SV707: $i,SV363: $i,SV125: $i,SV805: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV805 @ tc_HOL_Obool ) ) @ SV125 ) @ SV363 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV805 @ SV707 @ SV559 @ SV125 )
= $true )
| ( ( c_Fun_Oinj__on @ SV805 @ SV707 @ SV559 @ SV363 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7473]) ).
thf(7609,plain,
! [SV560: $i,SV126: $i,SV364: $i,SV708: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV708 ) @ SV364 ) @ SV126 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV708 ) @ SV560 ) @ SV126 ) )
= $true )
| ( ( SV560 = SV364 )
= $false )
| ( ( class_Orderings_Oord @ SV708 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7474]) ).
thf(7610,plain,
! [SV127: $i,SV365: $i,SV561: $i,SV709: $i,SV806: $i,SV859: $i,SV883: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV883 @ SV859 @ SV806 @ SV709 ) @ SV561 )
= SV365 )
= $false )
| ( ( ( hAPP @ SV709 @ ( hAPP @ SV561 @ SV127 ) )
= ( hAPP @ SV365 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7475]) ).
thf(7611,plain,
! [SV128: $i,SV366: $i,SV562: $i,SV710: $i,SV807: $i,SV860: $i] :
( ( ( SV860 != SV807 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV710 @ SV562 @ SV366 @ SV807 @ SV128 ) @ SV860 )
= SV128 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7476]) ).
thf(7612,plain,
! [SV128: $i,SV366: $i,SV562: $i,SV710: $i,SV807: $i,SV860: $i] :
( ( ~ ( ( SV860 != SV807 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV710 @ SV562 @ SV366 @ SV807 @ SV128 ) @ SV860 )
= ( hAPP @ SV366 @ SV860 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7477]) ).
thf(7613,plain,
! [SV129: $i,SV367: $i,SV563: $i,SV711: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV367 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV129 ) )
= $false )
| ( ( SV367 = SV129 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7478]) ).
thf(7614,plain,
! [SV563: $i,SV711: $i,SV129: $i,SV367: $i] :
( ( ( SV367 = SV129 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV367 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV711 ) @ SV563 ) @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7479]) ).
thf(7615,plain,
! [SV564: $i,SV130: $i,SV368: $i,SV712: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV712 ) @ SV368 ) @ SV130 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV712 ) @ SV564 ) @ SV130 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV712 ) @ SV564 ) @ SV368 ) )
= $false )
| ( ( class_Orderings_Opreorder @ SV712 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7480]) ).
thf(7616,plain,
! [SV565: $i,SV131: $i,SV713: $i,SV369: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV713 ) @ SV131 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV565 ) @ SV131 ) ) )
= $true )
| ( ( SV713 = SV565 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7481]) ).
thf(7617,plain,
! [SV713: $i,SV131: $i,SV565: $i,SV369: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV565 ) @ SV131 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV713 ) @ SV131 ) ) )
= $true )
| ( ( SV713 = SV565 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7482]) ).
thf(7618,plain,
! [SV566: $i,SV808: $i,SV132: $i,SV714: $i,SV861: $i,SV370: $i] :
( ( ( SV370
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV861 ) @ SV714 ) @ SV132 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV861 ) @ SV808 ) @ SV370 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV861 ) @ SV566 ) @ SV132 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV861 ) @ SV808 ) @ SV714 )
= SV566 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7483]) ).
thf(7619,plain,
! [SV133: $i,SV371: $i,SV567: $i,SV715: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV567 ) @ SV371 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV133 ) @ SV371 ) )
= $false )
| ( ( SV567 = SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7484]) ).
thf(7620,plain,
! [SV371: $i,SV715: $i,SV133: $i,SV567: $i] :
( ( ( SV567 = SV133 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV567 ) @ SV371 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV715 ) @ SV133 ) @ SV371 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7485]) ).
thf(7621,plain,
! [SV810: $i,SV862: $i,SV575: $i,SV142: $i,SV380: $i,SV720: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV720 @ SV380 ) @ SV142 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV575 @ SV380 ) @ SV142 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV862 @ ( tc_fun @ SV810 @ tc_HOL_Obool ) ) ) @ SV720 ) @ SV575 ) @ SV380 ) @ SV142 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7491]) ).
thf(7622,plain,
! [SV382: $i,SV577: $i,SV144: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV577 ) @ SV382 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV382 ) @ SV577 ) ) )
= $false )
| ( ( SV577 = SV382 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7493]) ).
thf(7623,plain,
! [SV382: $i,SV577: $i,SV144: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV577 ) @ SV382 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV382 ) @ SV577 ) ) )
= $true )
| ( ( SV577 = SV382 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7494]) ).
thf(7624,plain,
! [SV150: $i,SV388: $i,SV583: $i,SV811: $i,SV725: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV725 @ SV811 ) ) @ SV583 ) @ SV388 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV811 ) @ ( hAPP @ SV583 @ SV150 ) ) @ ( hAPP @ SV388 @ SV150 ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV811 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7497]) ).
thf(7625,plain,
! [SV813: $i,SV863: $i,SV152: $i,SV585: $i,SV390: $i,SV727: $i] :
( ( ( ( SV727 != SV390 )
| ( SV585 != SV152 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV863 @ SV813 ) @ SV727 ) @ SV585 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV863 @ SV813 ) @ SV390 ) @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7498]) ).
thf(7626,plain,
! [SV588: $i,SV155: $i,SV393: $i,SV730: $i,SV814: $i,SV864: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV864 @ SV814 ) @ SV730 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV393 @ ( tc_fun @ SV155 @ tc_HOL_Obool ) ) ) @ SV588 ) @ SV864 ) @ SV814 ) @ SV730 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7501]) ).
thf(7627,plain,
! [SV864: $i,SV155: $i,SV393: $i,SV730: $i,SV814: $i,SV588: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV588 @ SV814 ) @ SV730 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV393 @ ( tc_fun @ SV155 @ tc_HOL_Obool ) ) ) @ SV588 ) @ SV864 ) @ SV814 ) @ SV730 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7501]) ).
thf(7628,plain,
! [SV156: $i,SV394: $i,SV589: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
| ~ ( ( SV394 != SV156 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7502]) ).
thf(7629,plain,
! [SV156: $i,SV394: $i,SV589: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
| ~ ( ( SV394 != SV156 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7503]) ).
thf(7630,plain,
! [SV159: $i,SV397: $i,SV591: $i,SV732: $i,SV815: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV815 @ SV732 @ SV591 ) @ SV397 ) @ SV159 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV591 @ SV159 ) @ SV397 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7504]) ).
thf(7631,plain,
! [SV732: $i,SV815: $i,SV397: $i,SV159: $i,SV591: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV591 @ SV159 ) @ SV397 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV815 @ SV732 @ SV591 ) @ SV397 ) @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7505]) ).
thf(7632,plain,
! [SV816: $i,SV160: $i,SV398: $i,SV592: $i,SV733: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV592 ) @ SV398 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV398 ) @ SV160 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV592 ) @ SV160 ) ) )
= $true )
| ( ( c_Predicate_Otransp @ SV816 @ SV733 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7506]) ).
thf(7633,plain,
! [SV162: $i,SV400: $i,SV594: $i,SV817: $i,SV734: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV734 @ SV817 ) ) @ SV594 ) @ SV400 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV817 ) @ ( hAPP @ SV594 @ SV162 ) ) @ ( hAPP @ SV400 @ SV162 ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV817 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7509]) ).
thf(7634,plain,
! [SV401: $i,SV595: $i,SV163: $i,SV735: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV735 ) @ SV163 ) @ SV595 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV735 ) @ SV163 ) @ SV401 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV735 ) @ SV595 ) @ SV401 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV735 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7510]) ).
thf(7635,plain,
! [SV597: $i,SV737: $i,SV166: $i,SV404: $i] :
( ( ( SV404 != SV166 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV737 ) @ SV597 ) @ SV166 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV737 ) @ SV597 ) @ SV404 ) )
= $false )
| ( ( class_Orderings_Oord @ SV737 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7512]) ).
thf(7636,plain,
! [SV169: $i,SV407: $i,SV600: $i,SV739: $i,SV818: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) ) )
= $true )
| ( ( ~ ! [SY2478: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SY2478 ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SY2478 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7513]) ).
thf(7637,plain,
! [SV407: $i,SV818: $i,SV739: $i,SV169: $i,SV600: $i] :
( ( ( ~ ~ ! [SY2479: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SY2479 ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SY2479 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7514]) ).
thf(7638,plain,
! [SV409: $i,SV171: $i,SV602: $i,SV741: $i] :
( ( ( hBOOL @ ( hAPP @ SV741 @ SV602 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV171 @ tc_HOL_Obool ) ) @ SV409 ) @ SV741 ) @ SV602 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7516]) ).
thf(7639,plain,
! [SV607: $i,SV745: $i,SV178: $i,SV416: $i,SV820: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV416 ) @ SV178 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV745 ) @ SV416 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV607 ) @ SV178 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV745 ) @ SV607 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7520]) ).
thf(7640,plain,
! [SV179: $i,SV417: $i,SV608: $i,SV746: $i,SV821: $i,SV866: $i] :
( ( ( SV866 = SV821 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ SV608 ) @ SV866 ) @ SV417 ) ) @ SV821 ) @ SV179 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV746 @ SV608 ) @ SV821 ) @ SV179 ) ) @ SV866 ) @ SV417 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7521]) ).
thf(7641,plain,
! [SV181: $i,SV419: $i,SV610: $i,SV748: $i,SV823: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV823 @ SV748 @ SV610 ) @ SV419 ) @ SV181 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV610 @ SV181 ) @ SV419 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7522]) ).
thf(7642,plain,
! [SV748: $i,SV823: $i,SV419: $i,SV181: $i,SV610: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV610 @ SV181 ) @ SV419 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV823 @ SV748 @ SV610 ) @ SV419 ) @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7523]) ).
thf(7643,plain,
! [SV183: $i,SV421: $i,SV611: $i,SV749: $i,SV824: $i,SV867: $i,SV884: $i,SV891: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV891 @ SV884 @ SV867 @ SV824 ) @ SV749 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV611 @ SV884 @ SV867 @ SV421 ) @ SV183 ) )
= $true )
| ( ( ! [SY2485: $i] :
( ( hAPP @ SV824 @ ( hAPP @ SV749 @ SY2485 ) )
= ( hAPP @ SV421 @ ( hAPP @ SV183 @ SY2485 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7524]) ).
thf(7644,plain,
! [SV422: $i,SV899: $i,SV892: $i,SV184: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SV892 ) @ SV899 ) )
| ( ( hAPP @ SV184 @ SV892 )
= ( hAPP @ SV184 @ SV899 ) ) )
| ~ ( ( ( hAPP @ SV184 @ SV892 )
!= ( hAPP @ SV184 @ SV899 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SV892 ) @ SV899 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[7525]) ).
thf(7645,plain,
! [SV422: $i,SV184: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
| ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) ) )
| ~ ( ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
!= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ ( sK8_SY2542 @ SV422 @ SV184 ) ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[7526]) ).
thf(7646,plain,
! [SV186: $i,SV424: $i,SV613: $i,SV751: $i,SV826: $i,SV868: $i,SV885: $i,SV893: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV893 @ SV885 ) @ SV868 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV826 @ SV868 ) @ SV751 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV613 @ SV424 @ SV186 @ SV893 @ SV826 ) @ SV885 ) @ SV751 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7527]) ).
thf(7647,plain,
! [SV187: $i,SV425: $i,SV614: $i,SV752: $i,SV827: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV752 ) @ SV614 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV425 ) @ SV187 ) )
= $true )
| ( ( ~ ( ( SV752 != SV425 )
| ( SV614 != SV187 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7528]) ).
thf(7648,plain,
! [SV827: $i,SV187: $i,SV614: $i,SV425: $i,SV752: $i] :
( ( ( ~ ~ ( ( SV752 != SV425 )
| ( SV614 != SV187 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV752 ) @ SV614 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV425 ) @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7529]) ).
thf(7649,plain,
! [SV617: $i,SV754: $i,SV192: $i,SV430: $i,SV828: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ SV430 ) @ SV192 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ SV754 ) @ SV192 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ SV617 ) @ SV430 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV828 @ tc_HOL_Obool ) ) @ SV754 ) @ SV617 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7531]) ).
thf(7650,plain,
! [SV436: $i,SV198: $i,SV622: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV622 ) @ SV198 ) @ SV436 ) )
= $false )
| ( ( SV436 = SV198 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV622 ) @ SV436 ) @ SV198 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV622 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7535]) ).
thf(7651,plain,
! [SV440: $i,SV202: $i,SV625: $i] :
( ( ( hBOOL @ ( hAPP @ SV625 @ ( sK9_SY2261 @ SV202 @ SV440 @ SV625 ) ) )
= $false )
| ( ( ! [SY2262: $i,SY2263: $i] : ( hBOOL @ ( hAPP @ SV625 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV202 ) @ SY2262 ) @ SY2263 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[7538]) ).
thf(7652,plain,
! [SV202: $i,SV440: $i,SV625: $i] :
( ( ( ! [SY2545: $i] : ( hBOOL @ ( hAPP @ SV625 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV202 ) @ ( sK10_SY2264 @ SV202 @ SV440 @ SV625 ) ) @ SY2545 ) ) ) )
= $false )
| ( ( ! [SY2266: $i] : ( hBOOL @ ( hAPP @ SV625 @ SY2266 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[7539]) ).
thf(7653,plain,
! [SV441: $i,SV203: $i,SV626: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV203 ) @ SV441 ) )
| ( SV203 = SV441 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV441 ) @ SV203 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV626 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7540]) ).
thf(7654,plain,
! [SV626: $i,SV441: $i,SV203: $i] :
( ( ( ~ ( ( SV203 != SV441 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV203 ) @ SV441 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV441 ) @ SV203 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV626 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7540]) ).
thf(7655,plain,
! [SV829: $i,SV869: $i,SV627: $i,SV204: $i,SV442: $i,SV758: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV758 @ SV442 ) @ SV204 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV627 @ SV442 ) @ SV204 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV869 @ ( tc_fun @ SV829 @ tc_HOL_Obool ) ) ) @ SV758 ) @ SV627 ) @ SV442 ) @ SV204 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7541]) ).
thf(7656,plain,
! [SV759: $i,SV830: $i,SV208: $i,SV870: $i,SV446: $i,SV630: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV630 @ ( tc_fun @ SV446 @ tc_HOL_Obool ) ) ) @ SV870 ) @ SV208 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV208 @ SV830 ) @ SV759 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV870 @ SV830 ) @ SV759 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7542]) ).
thf(7657,plain,
! [SV451: $i,SV761: $i,SV213: $i,SV634: $i] :
( ( ( SV634 != SV213 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV761 ) @ SV213 ) @ SV451 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV761 ) @ SV634 ) @ SV451 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV761 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7543]) ).
thf(7658,plain,
! [SV216: $i,SV454: $i,SV637: $i,SV763: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV763 ) @ SV637 ) @ SV454 ) @ SV216 ) )
= $false )
| ( ( ( SV637 = SV216 )
| ( hBOOL @ ( hAPP @ SV454 @ SV216 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7545]) ).
thf(7659,plain,
! [SV763: $i,SV454: $i,SV216: $i,SV637: $i] :
( ( ( ( SV637 = SV216 )
| ( hBOOL @ ( hAPP @ SV454 @ SV216 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV763 ) @ SV637 ) @ SV454 ) @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7546]) ).
thf(7660,plain,
! [SV217: $i,SV455: $i,SV638: $i,SV764: $i,SV832: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $true )
| ( ( ~ ! [SY2491: $i] :
~ ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SY2491 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2491 ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SY2491 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2491 ) @ SV217 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7547]) ).
thf(7661,plain,
! [SV217: $i,SV638: $i,SV455: $i,SV832: $i,SV764: $i] :
( ( ( ~ ~ ! [SY2492: $i] :
~ ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SY2492 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2492 ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SY2492 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2492 ) @ SV217 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7548]) ).
thf(7662,plain,
! [SV834: $i,SV225: $i,SV463: $i,SV644: $i,SV768: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV644 ) @ SV463 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV463 ) @ SV225 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV644 ) @ SV225 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV834 @ SV768 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7554]) ).
thf(7663,plain,
! [SV226: $i,SV464: $i,SV645: $i,SV769: $i,SV835: $i,SV871: $i,SV886: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
| ~ ! [SY2430: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SY2430 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2430 ) @ SV226 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7555]) ).
thf(7664,plain,
! [SV835: $i,SV871: $i,SV886: $i,SV226: $i,SV645: $i,SV464: $i,SV769: $i] :
( ( ~ ( ~ ~ ! [SY2431: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SY2431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2431 ) @ SV226 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7555]) ).
thf(7665,plain,
! [SV227: $i,SV465: $i,SV646: $i,SV770: $i,SV836: $i,SV872: $i,SV887: $i] :
( ( ( c_Finite__Set_Ofolding__image__simple__idem @ SV887 @ SV872 @ SV836 @ SV770 @ SV646 @ SV465 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV836 @ SV227 ) @ SV227 )
= SV227 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7556]) ).
thf(7666,plain,
! [SV649: $i,SV468: $i,SV230: $i,SV773: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV773 ) @ SV230 ) @ SV468 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV773 ) @ SV230 ) @ SV649 ) )
= $true )
| ( ( SV649 = SV468 )
= $false )
| ( ( class_Orderings_Oorder @ SV773 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7559]) ).
thf(7667,plain,
! [SV469: $i,SV231: $i,SV650: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV650 ) @ SV231 ) @ SV469 ) )
= $false )
| ( ( SV231 = SV469 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV650 ) @ SV469 ) @ SV231 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV650 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7560]) ).
thf(7668,plain,
! [SV775: $i,SV472: $i,SV234: $i,SV652: $i] :
( ( ( hBOOL @ ( hAPP @ SV652 @ SV234 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV472 @ SV234 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV775 @ tc_HOL_Obool ) ) @ SV652 ) @ SV472 ) @ SV234 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7562]) ).
thf(7669,plain,
! [SV235: $i,SV473: $i,SV653: $i,SV776: $i,SV839: $i,SV875: $i,SV888: $i] :
( ( ( c_Typedef_Otype__definition @ SV888 @ SV875 @ SV839 @ SV776 @ SV653 )
= $false )
| ( ( ~ ( ~ ( ( ( hAPP @ SV839 @ SV473 )
!= ( hAPP @ SV839 @ SV235 ) )
| ( SV473 = SV235 ) )
| ~ ( ( SV473 != SV235 )
| ( ( hAPP @ SV839 @ SV473 )
= ( hAPP @ SV839 @ SV235 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7563]) ).
thf(7670,plain,
! [SV474: $i,SV777: $i,SV236: $i,SV654: $i] :
( ( ( hBOOL @ ( hAPP @ SV654 @ SV236 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV777 @ tc_HOL_Obool ) ) @ SV654 ) @ SV474 ) @ SV236 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7564]) ).
thf(7671,plain,
! [SV654: $i,SV777: $i,SV236: $i,SV474: $i] :
( ( ( hBOOL @ ( hAPP @ SV474 @ SV236 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV777 @ tc_HOL_Obool ) ) @ SV654 ) @ SV474 ) @ SV236 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7565]) ).
thf(7672,plain,
! [SV660: $i,SV243: $i,SV481: $i] :
( ( ( SV481 != SV243 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV660 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7567]) ).
thf(7673,plain,
! [SV243: $i,SV481: $i,SV660: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) ) ) )
= $true )
| ( ( SV481 = SV243 )
= $true )
| ( ( class_Orderings_Oorder @ SV660 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7568]) ).
thf(7674,plain,
! [SV519: $i,SV682: $i,SV69: $i,SV308: $i] :
( ( ( ! [SY1684: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ SY1684 ) @ SV69 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV682 @ SV519 @ SV308 ) @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7569]) ).
thf(7675,plain,
! [SV519: $i,SV682: $i,SV69: $i,SV308: $i] :
( ( ( ! [SY1685: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ SY1685 ) @ SV69 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV682 @ SV519 @ SV308 ) @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7570]) ).
thf(7676,plain,
! [SV309: $i,SV70: $i] :
( ( ( ~ ! [SY1062: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1062 ) @ SY1062 ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7571]) ).
thf(7677,plain,
! [SV309: $i,SV70: $i] :
( ( ( ! [SY1063: $i,SY1064: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1064 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1064 ) @ SY1064 ) ) )
| ( ( hAPP @ SV70 @ SY1063 )
!= ( hAPP @ SV70 @ SY1064 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1064 ) @ SY1064 ) ) )
| ( ( hAPP @ SV70 @ SY1063 )
!= ( hAPP @ SV70 @ SY1064 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1063 ) @ SY1064 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7572]) ).
thf(7678,plain,
! [SV309: $i,SV70: $i] :
( ( ( ~ ! [SY1065: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1065 ) @ SY1065 ) ) )
= $false )
| ( ( ~ ! [SY1066: $i,SY1067: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7573]) ).
thf(7679,plain,
! [SV520: $i,SV683: $i,SV71: $i,SV310: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV683 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV520 ) )
= $true )
| ( ( SV683 = SV520 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7574]) ).
thf(7680,plain,
! [SV683: $i,SV520: $i,SV71: $i,SV310: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV520 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV683 ) )
= $true )
| ( ( SV683 = SV520 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7575]) ).
thf(7681,plain,
! [SV73: $i,SV312: $i,SV521: $i,SV684: $i,SV789: $i,SV848: $i,SV880: $i,SV889: $i,SV894: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV894 @ SV889 @ SV880 @ SV848 ) @ SV789 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV684 @ SV889 @ SV880 @ SV521 ) @ SV312 ) )
= $true )
| ( ( ( hAPP @ SV848 @ ( hAPP @ SV789 @ SV73 ) )
= ( hAPP @ SV521 @ ( hAPP @ SV312 @ SV73 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7576]) ).
thf(7682,plain,
! [SV849: $i,SV75: $i,SV314: $i,SV686: $i,SV790: $i,SV523: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV523 @ SV790 ) @ SV686 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV314 @ ( tc_fun @ SV75 @ tc_HOL_Obool ) ) ) @ SV849 ) @ SV523 ) @ SV790 ) @ SV686 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV849 @ SV790 ) @ SV686 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7578]) ).
thf(7683,plain,
! [SV881: $i,SV529: $i,SV85: $i,SV323: $i] :
( ( ( SV323
= ( c_Hilbert__Choice_OEps @ SV85 @ SV529 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV529 @ SV323 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV529 @ SV881 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7579]) ).
thf(7684,plain,
! [SV530: $i,SV689: $i,SV86: $i,SV324: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
= $true )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) ) ) )
= $true )
| ( ( SV689 = SV530 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7580]) ).
thf(7685,plain,
! [SV689: $i,SV530: $i,SV86: $i,SV324: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) )
= $true )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) ) ) )
= $true )
| ( ( SV689 = SV530 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7581]) ).
thf(7686,plain,
! [SV792: $i,SV850: $i,SV532: $i,SV88: $i,SV326: $i,SV691: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV691 @ SV326 ) @ SV88 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV532 @ SV326 ) @ SV88 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV850 @ ( tc_fun @ SV792 @ tc_HOL_Obool ) ) ) @ SV691 ) @ SV532 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7582]) ).
thf(7687,plain,
! [SV535: $i,SV693: $i,SV92: $i,SV330: $i] :
( ( ( ! [SY1733: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ SY1733 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV693 @ SV535 @ SV330 ) @ SV92 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7584]) ).
thf(7688,plain,
! [SV535: $i,SV693: $i,SV92: $i,SV330: $i] :
( ( ( ! [SY1734: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ SY1734 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV693 @ SV535 @ SV330 ) @ SV92 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7585]) ).
thf(7689,plain,
! [SV99: $i,SV337: $i,SV540: $i,SV696: $i,SV796: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV796 @ SV696 @ SV540 ) @ SV337 ) @ SV99 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV337 @ ( hAPP @ SV540 @ SV99 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7587]) ).
thf(7690,plain,
! [SV696: $i,SV796: $i,SV99: $i,SV540: $i,SV337: $i] :
( ( ( hBOOL @ ( hAPP @ SV337 @ ( hAPP @ SV540 @ SV99 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV796 @ SV696 @ SV540 ) @ SV337 ) @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7588]) ).
thf(7691,plain,
! [SV100: $i,SV338: $i,SV541: $i,SV697: $i,SV797: $i,SV853: $i,SV882: $i,SV890: $i,SV895: $i,SV900: $i] :
( ( ! [SY2546: $i] :
( ( ( hAPP @ SY2546 @ ( hAPP @ SV900 @ SV895 ) )
!= ( hAPP @ SV890 @ ( hAPP @ SV882 @ SV853 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV797 @ SV697 @ SV541 @ SY2546 ) @ SV900 ) @ SV895 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV338 @ SV697 @ SV100 @ SV890 ) @ SV882 ) @ SV853 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7589]) ).
thf(7692,plain,
! [SV544: $i,SV103: $i,SV896: $i,SV341: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV896 ) @ SV103 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV896 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV103 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7590]) ).
thf(7693,plain,
! [SV103: $i,SV544: $i,SV341: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ ( sK5_SY2146 @ SV544 @ SV103 @ SV341 ) ) @ SV103 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV103 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7591]) ).
thf(7694,plain,
! [SV103: $i,SV341: $i,SV544: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ ( sK5_SY2146 @ SV544 @ SV103 @ SV341 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV103 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7591]) ).
thf(7695,plain,
! [SV799: $i,SV546: $i,SV105: $i,SV343: $i,SV699: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV343 ) @ SV105 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV546 ) @ SV105 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV546 ) @ SV343 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV799 @ SV699 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7592]) ).
thf(7696,plain,
! [SV110: $i,SV348: $i,SV548: $i,SV701: $i,SV801: $i] :
( ( ( ( c_Fun_Ofun__upd @ SV801 @ SV701 @ SV548 @ SV348 @ SV110 )
= SV548 )
= $false )
| ( ( ( hAPP @ SV548 @ SV348 )
= SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7593]) ).
thf(7697,plain,
! [SV701: $i,SV801: $i,SV110: $i,SV348: $i,SV548: $i] :
( ( ( ( hAPP @ SV548 @ SV348 )
= SV110 )
= $false )
| ( ( ( c_Fun_Ofun__upd @ SV801 @ SV701 @ SV548 @ SV348 @ SV110 )
= SV548 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7594]) ).
thf(7698,plain,
! [SV550: $i,SV112: $i,SV897: $i,SV350: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV350 @ SV897 ) @ SV112 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV897 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV112 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7595]) ).
thf(7699,plain,
! [SV112: $i,SV550: $i,SV350: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV350 @ ( sK6_SY2154 @ SV550 @ SV112 @ SV350 ) ) @ SV112 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7596]) ).
thf(7700,plain,
! [SV112: $i,SV350: $i,SV550: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ ( sK6_SY2154 @ SV550 @ SV112 @ SV350 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7596]) ).
thf(7701,plain,
! [SV114: $i,SV352: $i,SV552: $i,SV703: $i,SV802: $i,SV856: $i] :
( ( ( SV856 != SV802 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV703 @ SV552 @ SV352 @ SV802 @ SV114 ) @ SV856 )
= SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7597]) ).
thf(7702,plain,
! [SV114: $i,SV352: $i,SV552: $i,SV703: $i,SV802: $i,SV856: $i] :
( ( ( ~ ( ( SV856 != SV802 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV703 @ SV552 @ SV352 @ SV802 @ SV114 ) @ SV856 )
= ( hAPP @ SV352 @ SV856 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7598]) ).
thf(7703,plain,
! [SV117: $i,SV355: $i,SV554: $i,SV704: $i,SV803: $i,SV857: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV704 ) @ SV554 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV355 ) @ SV117 ) )
= $true )
| ( ( ~ ( ( SV704 != SV355 )
| ( SV554 != SV117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7599]) ).
thf(7704,plain,
! [SV803: $i,SV857: $i,SV117: $i,SV554: $i,SV355: $i,SV704: $i] :
( ( ( ~ ~ ( ( SV704 != SV355 )
| ( SV554 != SV117 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV704 ) @ SV554 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV355 ) @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7600]) ).
thf(7705,plain,
! [SV121: $i,SV359: $i,SV706: $i,SV557: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV557 @ SV706 ) ) @ SV359 ) @ SV121 ) ) )
= $true )
| ( ( ! [SY2373: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV706 ) @ ( hAPP @ SV359 @ SY2373 ) ) @ ( hAPP @ SV121 @ SY2373 ) ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV706 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7604]) ).
thf(7706,plain,
! [SV557: $i,SV121: $i,SV359: $i,SV706: $i] :
( ( ( ~ ! [SY2374: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV706 ) @ ( hAPP @ SV359 @ SY2374 ) ) @ ( hAPP @ SV121 @ SY2374 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV557 @ SV706 ) ) @ SV359 ) @ SV121 ) )
= $true )
| ( ( class_Orderings_Oord @ SV706 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7605]) ).
thf(7707,plain,
! [SV123: $i,SV361: $i] :
( ( ( hBOOL @ ( hAPP @ SV361 @ ( sK7_SY1800 @ SV123 @ SV361 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV361 @ ( c_Hilbert__Choice_OEps @ SV123 @ SV361 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7606]) ).
thf(7708,plain,
! [SV123: $i,SV898: $i,SV361: $i] :
( ( ( hBOOL @ ( hAPP @ SV361 @ SV898 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV361 @ ( c_Hilbert__Choice_OEps @ SV123 @ SV361 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7607]) ).
thf(7709,plain,
! [SV560: $i,SV126: $i,SV364: $i,SV708: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV708 ) @ SV364 ) @ SV126 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV708 ) @ SV560 ) @ SV126 ) )
= $true )
| ( ( SV560 = SV364 )
= $false )
| ( ( class_Orderings_Oord @ SV708 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7609]) ).
thf(7710,plain,
! [SV128: $i,SV366: $i,SV562: $i,SV710: $i,SV807: $i,SV860: $i] :
( ( ( SV860 != SV807 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV710 @ SV562 @ SV366 @ SV807 @ SV128 ) @ SV860 )
= SV128 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7611]) ).
thf(7711,plain,
! [SV128: $i,SV366: $i,SV562: $i,SV710: $i,SV807: $i,SV860: $i] :
( ( ( ~ ( ( SV860 != SV807 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV710 @ SV562 @ SV366 @ SV807 @ SV128 ) @ SV860 )
= ( hAPP @ SV366 @ SV860 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7612]) ).
thf(7712,plain,
! [SV564: $i,SV130: $i,SV368: $i,SV712: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV712 ) @ SV368 ) @ SV130 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV712 ) @ SV564 ) @ SV130 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV712 ) @ SV564 ) @ SV368 ) )
= $false )
| ( ( class_Orderings_Opreorder @ SV712 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7615]) ).
thf(7713,plain,
! [SV565: $i,SV131: $i,SV713: $i,SV369: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV713 ) @ SV131 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV565 ) @ SV131 ) )
= $true )
| ( ( SV713 = SV565 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7616]) ).
thf(7714,plain,
! [SV713: $i,SV131: $i,SV565: $i,SV369: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV565 ) @ SV131 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV713 ) @ SV131 ) )
= $true )
| ( ( SV713 = SV565 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7617]) ).
thf(7715,plain,
! [SV566: $i,SV808: $i,SV132: $i,SV714: $i,SV861: $i,SV370: $i] :
( ( ( SV370
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV861 ) @ SV714 ) @ SV132 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV861 ) @ SV808 ) @ SV370 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV861 ) @ SV566 ) @ SV132 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV861 ) @ SV808 ) @ SV714 )
= SV566 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7618]) ).
thf(7716,plain,
! [SV575: $i,SV810: $i,SV862: $i,SV142: $i,SV380: $i,SV720: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV720 @ SV380 ) @ SV142 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV862 @ ( tc_fun @ SV810 @ tc_HOL_Obool ) ) ) @ SV720 ) @ SV575 ) @ SV380 ) @ SV142 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7621]) ).
thf(7717,plain,
! [SV720: $i,SV810: $i,SV862: $i,SV142: $i,SV380: $i,SV575: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV575 @ SV380 ) @ SV142 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV862 @ ( tc_fun @ SV810 @ tc_HOL_Obool ) ) ) @ SV720 ) @ SV575 ) @ SV380 ) @ SV142 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7621]) ).
thf(7718,plain,
! [SV382: $i,SV577: $i,SV144: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV577 ) @ SV382 ) ) )
= $false )
| ( ( SV577 = SV382 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7622]) ).
thf(7719,plain,
! [SV577: $i,SV382: $i,SV144: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV382 ) @ SV577 ) ) )
= $false )
| ( ( SV577 = SV382 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7622]) ).
thf(7720,plain,
! [SV382: $i,SV577: $i,SV144: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV577 ) @ SV382 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV382 ) @ SV577 ) ) )
= $true )
| ( ( SV577 = SV382 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7623]) ).
thf(7721,plain,
! [SV152: $i,SV585: $i,SV813: $i,SV863: $i,SV390: $i,SV727: $i] :
( ( ( SV727 != SV390 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV863 @ SV813 ) @ SV727 ) @ SV585 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV863 @ SV813 ) @ SV390 ) @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7625]) ).
thf(7722,plain,
! [SV390: $i,SV727: $i,SV813: $i,SV863: $i,SV152: $i,SV585: $i] :
( ( ( SV585 != SV152 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV863 @ SV813 ) @ SV727 ) @ SV585 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV863 @ SV813 ) @ SV390 ) @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7625]) ).
thf(7723,plain,
! [SV588: $i,SV155: $i,SV393: $i,SV730: $i,SV814: $i,SV864: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV864 @ SV814 ) @ SV730 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV393 @ ( tc_fun @ SV155 @ tc_HOL_Obool ) ) ) @ SV588 ) @ SV864 ) @ SV814 ) @ SV730 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7626]) ).
thf(7724,plain,
! [SV156: $i,SV394: $i,SV589: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7628]) ).
thf(7725,plain,
! [SV589: $i,SV156: $i,SV394: $i] :
( ( ( ~ ( ( SV394 != SV156 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7628]) ).
thf(7726,plain,
! [SV156: $i,SV394: $i,SV589: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) ) )
= $true )
| ( ( ~ ( ( SV394 != SV156 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7629]) ).
thf(7727,plain,
! [SV159: $i,SV397: $i,SV591: $i,SV732: $i,SV815: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV815 @ SV732 @ SV591 ) @ SV397 ) @ SV159 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV591 @ SV159 ) @ SV397 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7630]) ).
thf(7728,plain,
! [SV732: $i,SV815: $i,SV397: $i,SV159: $i,SV591: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV591 @ SV159 ) @ SV397 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV815 @ SV732 @ SV591 ) @ SV397 ) @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7631]) ).
thf(7729,plain,
! [SV816: $i,SV592: $i,SV160: $i,SV398: $i,SV733: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV398 ) @ SV160 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV592 ) @ SV160 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV592 ) @ SV398 ) )
= $false )
| ( ( c_Predicate_Otransp @ SV816 @ SV733 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7632]) ).
thf(7730,plain,
! [SV401: $i,SV595: $i,SV163: $i,SV735: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV735 ) @ SV163 ) @ SV595 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV735 ) @ SV163 ) @ SV401 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV735 ) @ SV595 ) @ SV401 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV735 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7634]) ).
thf(7731,plain,
! [SV597: $i,SV737: $i,SV166: $i,SV404: $i] :
( ( ( SV404 = SV166 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV737 ) @ SV597 ) @ SV166 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV737 ) @ SV597 ) @ SV404 ) )
= $false )
| ( ( class_Orderings_Oord @ SV737 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7635]) ).
thf(7732,plain,
! [SV169: $i,SV407: $i,SV600: $i,SV739: $i,SV818: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
= $false )
| ( ( ~ ! [SY2478: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SY2478 ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SY2478 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7636]) ).
thf(7733,plain,
! [SV407: $i,SV818: $i,SV739: $i,SV169: $i,SV600: $i] :
( ( ( ~ ! [SY2479: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SY2479 ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SY2479 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7637]) ).
thf(7734,plain,
! [SV181: $i,SV419: $i,SV610: $i,SV748: $i,SV823: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV823 @ SV748 @ SV610 ) @ SV419 ) @ SV181 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV610 @ SV181 ) @ SV419 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7641]) ).
thf(7735,plain,
! [SV748: $i,SV823: $i,SV419: $i,SV181: $i,SV610: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV610 @ SV181 ) @ SV419 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV823 @ SV748 @ SV610 ) @ SV419 ) @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7642]) ).
thf(7736,plain,
! [SV183: $i,SV421: $i,SV611: $i,SV749: $i,SV824: $i,SV867: $i,SV884: $i,SV891: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV891 @ SV884 @ SV867 @ SV824 ) @ SV749 )
= ( hAPP @ ( c_Fun_Ocomp @ SV611 @ SV884 @ SV867 @ SV421 ) @ SV183 ) )
= $false )
| ( ( ! [SY2485: $i] :
( ( hAPP @ SV824 @ ( hAPP @ SV749 @ SY2485 ) )
= ( hAPP @ SV421 @ ( hAPP @ SV183 @ SY2485 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7643]) ).
thf(7737,plain,
! [SV422: $i,SV899: $i,SV892: $i,SV184: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SV892 ) @ SV899 ) )
| ( ( hAPP @ SV184 @ SV892 )
= ( hAPP @ SV184 @ SV899 ) ) )
| ~ ( ( ( hAPP @ SV184 @ SV892 )
!= ( hAPP @ SV184 @ SV899 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SV892 ) @ SV899 ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7644]) ).
thf(7738,plain,
! [SV422: $i,SV184: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
| ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) ) )
| ~ ( ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
!= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ ( sK8_SY2542 @ SV422 @ SV184 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7645]) ).
thf(7739,plain,
! [SV186: $i,SV424: $i,SV613: $i,SV751: $i,SV826: $i,SV868: $i,SV885: $i,SV893: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV893 @ SV885 ) @ SV868 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV826 @ SV868 ) @ SV751 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV613 @ SV424 @ SV186 @ SV893 @ SV826 ) @ SV885 ) @ SV751 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7646]) ).
thf(7740,plain,
! [SV187: $i,SV425: $i,SV614: $i,SV752: $i,SV827: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV752 ) @ SV614 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV425 ) @ SV187 ) )
= $false )
| ( ( ~ ( ( SV752 != SV425 )
| ( SV614 != SV187 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7647]) ).
thf(7741,plain,
! [SV827: $i,SV187: $i,SV614: $i,SV425: $i,SV752: $i] :
( ( ( ~ ( ( SV752 != SV425 )
| ( SV614 != SV187 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV752 ) @ SV614 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV425 ) @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7648]) ).
thf(7742,plain,
! [SV901: $i,SV202: $i,SV440: $i,SV625: $i] :
( ( ( ! [SY2547: $i] : ( hBOOL @ ( hAPP @ SV625 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV202 ) @ SV901 ) @ SY2547 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV625 @ ( sK9_SY2261 @ SV202 @ SV440 @ SV625 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[7651]) ).
thf(7743,plain,
! [SV202: $i,SV440: $i,SV625: $i] :
( ( ( hBOOL @ ( hAPP @ SV625 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV202 ) @ ( sK10_SY2264 @ SV202 @ SV440 @ SV625 ) ) @ ( sK11_SY2545 @ SV202 @ SV440 @ SV625 ) ) ) )
= $false )
| ( ( ! [SY2266: $i] : ( hBOOL @ ( hAPP @ SV625 @ SY2266 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[7652]) ).
thf(7744,plain,
! [SV441: $i,SV203: $i,SV626: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV203 ) @ SV441 ) )
| ( SV203 = SV441 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV441 ) @ SV203 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV626 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7653]) ).
thf(7745,plain,
! [SV626: $i,SV441: $i,SV203: $i] :
( ( ( ( SV203 != SV441 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV203 ) @ SV441 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV441 ) @ SV203 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV626 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7654]) ).
thf(7746,plain,
! [SV829: $i,SV869: $i,SV627: $i,SV204: $i,SV442: $i,SV758: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV758 @ SV442 ) @ SV204 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV627 @ SV442 ) @ SV204 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV869 @ ( tc_fun @ SV829 @ tc_HOL_Obool ) ) ) @ SV758 ) @ SV627 ) @ SV442 ) @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7655]) ).
thf(7747,plain,
! [SV759: $i,SV830: $i,SV208: $i,SV870: $i,SV446: $i,SV630: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV630 @ ( tc_fun @ SV446 @ tc_HOL_Obool ) ) ) @ SV870 ) @ SV208 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV208 @ SV830 ) @ SV759 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV870 @ SV830 ) @ SV759 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7656]) ).
thf(7748,plain,
! [SV451: $i,SV761: $i,SV213: $i,SV634: $i] :
( ( ( SV634 = SV213 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV761 ) @ SV213 ) @ SV451 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV761 ) @ SV634 ) @ SV451 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV761 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7657]) ).
thf(7749,plain,
! [SV763: $i,SV454: $i,SV216: $i,SV637: $i] :
( ( ( SV637 = SV216 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV454 @ SV216 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV763 ) @ SV637 ) @ SV454 ) @ SV216 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7658]) ).
thf(7750,plain,
! [SV454: $i,SV763: $i,SV216: $i,SV637: $i] :
( ( ( SV637 = SV216 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV763 ) @ SV637 ) @ SV454 ) @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7659]) ).
thf(7751,plain,
! [SV637: $i,SV763: $i,SV216: $i,SV454: $i] :
( ( ( hBOOL @ ( hAPP @ SV454 @ SV216 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV763 ) @ SV637 ) @ SV454 ) @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7659]) ).
thf(7752,plain,
! [SV217: $i,SV455: $i,SV638: $i,SV764: $i,SV832: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $false )
| ( ( ~ ! [SY2491: $i] :
~ ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SY2491 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2491 ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SY2491 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2491 ) @ SV217 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7660]) ).
thf(7753,plain,
! [SV217: $i,SV638: $i,SV455: $i,SV832: $i,SV764: $i] :
( ( ( ~ ! [SY2492: $i] :
~ ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SY2492 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2492 ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SY2492 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2492 ) @ SV217 ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7661]) ).
thf(7754,plain,
! [SV834: $i,SV644: $i,SV225: $i,SV463: $i,SV768: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV463 ) @ SV225 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV644 ) @ SV225 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV644 ) @ SV463 ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV834 @ SV768 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7662]) ).
thf(7755,plain,
! [SV226: $i,SV464: $i,SV645: $i,SV769: $i,SV835: $i,SV871: $i,SV886: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
| ~ ! [SY2430: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SY2430 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2430 ) @ SV226 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7663]) ).
thf(7756,plain,
! [SV835: $i,SV871: $i,SV886: $i,SV226: $i,SV645: $i,SV464: $i,SV769: $i] :
( ( ~ ~ ! [SY2431: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SY2431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2431 ) @ SV226 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7664]) ).
thf(7757,plain,
! [SV649: $i,SV468: $i,SV230: $i,SV773: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV773 ) @ SV230 ) @ SV468 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV773 ) @ SV230 ) @ SV649 ) )
= $true )
| ( ( SV649 = SV468 )
= $false )
| ( ( class_Orderings_Oorder @ SV773 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7666]) ).
thf(7758,plain,
! [SV653: $i,SV776: $i,SV875: $i,SV888: $i,SV235: $i,SV473: $i,SV839: $i] :
( ( ( ~ ( ( ( hAPP @ SV839 @ SV473 )
!= ( hAPP @ SV839 @ SV235 ) )
| ( SV473 = SV235 ) )
| ~ ( ( SV473 != SV235 )
| ( ( hAPP @ SV839 @ SV473 )
= ( hAPP @ SV839 @ SV235 ) ) ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV888 @ SV875 @ SV839 @ SV776 @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7669]) ).
thf(7759,plain,
! [SV660: $i,SV243: $i,SV481: $i] :
( ( ( SV481 = SV243 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7672]) ).
thf(7760,plain,
! [SV243: $i,SV481: $i,SV660: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) ) ) )
= $false )
| ( ( SV481 = SV243 )
= $true )
| ( ( class_Orderings_Oorder @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7673]) ).
thf(7761,plain,
! [SV69: $i,SV682: $i,SV519: $i,SV308: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ ( sK12_SY1684 @ SV519 @ SV682 @ SV69 @ SV308 ) ) @ SV69 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV682 @ SV519 @ SV308 ) @ SV69 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[7674]) ).
thf(7762,plain,
! [SV519: $i,SV682: $i,SV69: $i,SV902: $i,SV308: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ SV902 ) @ SV69 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV682 @ SV519 @ SV308 ) @ SV69 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[7675]) ).
thf(7763,plain,
! [SV309: $i,SV70: $i] :
( ( ( ! [SY1062: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1062 ) @ SY1062 ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7676]) ).
thf(7764,plain,
! [SV309: $i,SV903: $i,SV70: $i] :
( ( ( ! [SY2548: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SY2548 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY2548 ) @ SY2548 ) ) )
| ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SY2548 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY2548 ) @ SY2548 ) ) )
| ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SY2548 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SY2548 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[7677]) ).
thf(7765,plain,
! [SV309: $i,SV70: $i] :
( ( ( ! [SY1065: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1065 ) @ SY1065 ) ) )
= $true )
| ( ( ~ ! [SY1066: $i,SY1067: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7678]) ).
thf(7766,plain,
! [SV520: $i,SV683: $i,SV71: $i,SV310: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV683 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV520 ) )
= $true )
| ( ( SV683 = SV520 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7679]) ).
thf(7767,plain,
! [SV683: $i,SV520: $i,SV71: $i,SV310: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV520 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV310 ) @ SV71 ) @ SV683 ) )
= $true )
| ( ( SV683 = SV520 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7680]) ).
thf(7768,plain,
! [SV73: $i,SV312: $i,SV521: $i,SV684: $i,SV789: $i,SV848: $i,SV880: $i,SV889: $i,SV894: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV894 @ SV889 @ SV880 @ SV848 ) @ SV789 )
= ( hAPP @ ( c_Fun_Ocomp @ SV684 @ SV889 @ SV880 @ SV521 ) @ SV312 ) )
= $false )
| ( ( ( hAPP @ SV848 @ ( hAPP @ SV789 @ SV73 ) )
= ( hAPP @ SV521 @ ( hAPP @ SV312 @ SV73 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7681]) ).
thf(7769,plain,
! [SV530: $i,SV689: $i,SV86: $i,SV324: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
= $true )
| ( ( SV689 = SV530 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7684]) ).
thf(7770,plain,
! [SV530: $i,SV689: $i,SV86: $i,SV324: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) )
= $true )
| ( ( SV689 = SV530 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7685]) ).
thf(7771,plain,
! [SV693: $i,SV535: $i,SV92: $i,SV330: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ ( sK13_SY1733 @ SV535 @ SV693 @ SV92 @ SV330 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV693 @ SV535 @ SV330 ) @ SV92 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[7687]) ).
thf(7772,plain,
! [SV535: $i,SV693: $i,SV904: $i,SV92: $i,SV330: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ SV904 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV693 @ SV535 @ SV330 ) @ SV92 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[7688]) ).
thf(7773,plain,
! [SV100: $i,SV338: $i,SV541: $i,SV697: $i,SV797: $i,SV853: $i,SV882: $i,SV890: $i,SV895: $i,SV900: $i,SV905: $i] :
( ( ( ( hAPP @ SV905 @ ( hAPP @ SV900 @ SV895 ) )
!= ( hAPP @ SV890 @ ( hAPP @ SV882 @ SV853 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV797 @ SV697 @ SV541 @ SV905 ) @ SV900 ) @ SV895 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV338 @ SV697 @ SV100 @ SV890 ) @ SV882 ) @ SV853 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7691]) ).
thf(7774,plain,
! [SV544: $i,SV103: $i,SV896: $i,SV341: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV896 ) @ SV103 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV896 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV103 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7692]) ).
thf(7775,plain,
! [SV103: $i,SV544: $i,SV341: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ ( sK5_SY2146 @ SV544 @ SV103 @ SV341 ) ) @ SV103 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV544 @ SV341 ) @ SV103 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7693]) ).
thf(7776,plain,
! [SV799: $i,SV546: $i,SV105: $i,SV343: $i,SV699: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV343 ) @ SV105 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV546 ) @ SV105 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV699 @ SV546 ) @ SV343 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV799 @ SV699 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7695]) ).
thf(7777,plain,
! [SV550: $i,SV112: $i,SV897: $i,SV350: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV350 @ SV897 ) @ SV112 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV897 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7698]) ).
thf(7778,plain,
! [SV112: $i,SV550: $i,SV350: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV350 @ ( sK6_SY2154 @ SV550 @ SV112 @ SV350 ) ) @ SV112 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV550 @ SV350 ) @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7699]) ).
thf(7779,plain,
! [SV114: $i,SV352: $i,SV552: $i,SV703: $i,SV802: $i,SV856: $i] :
( ( ( SV856 = SV802 )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV703 @ SV552 @ SV352 @ SV802 @ SV114 ) @ SV856 )
= SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7701]) ).
thf(7780,plain,
! [SV114: $i,SV352: $i,SV552: $i,SV703: $i,SV802: $i,SV856: $i] :
( ( ( SV856 != SV802 )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV703 @ SV552 @ SV352 @ SV802 @ SV114 ) @ SV856 )
= ( hAPP @ SV352 @ SV856 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7702]) ).
thf(7781,plain,
! [SV117: $i,SV355: $i,SV554: $i,SV704: $i,SV803: $i,SV857: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV704 ) @ SV554 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV355 ) @ SV117 ) )
= $false )
| ( ( ~ ( ( SV704 != SV355 )
| ( SV554 != SV117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7703]) ).
thf(7782,plain,
! [SV803: $i,SV857: $i,SV117: $i,SV554: $i,SV355: $i,SV704: $i] :
( ( ( ~ ( ( SV704 != SV355 )
| ( SV554 != SV117 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV704 ) @ SV554 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV355 ) @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7704]) ).
thf(7783,plain,
! [SV121: $i,SV359: $i,SV706: $i,SV557: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV557 @ SV706 ) ) @ SV359 ) @ SV121 ) )
= $false )
| ( ( ! [SY2373: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV706 ) @ ( hAPP @ SV359 @ SY2373 ) ) @ ( hAPP @ SV121 @ SY2373 ) ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV706 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7705]) ).
thf(7784,plain,
! [SV557: $i,SV121: $i,SV359: $i,SV706: $i] :
( ( ( ! [SY2374: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV706 ) @ ( hAPP @ SV359 @ SY2374 ) ) @ ( hAPP @ SV121 @ SY2374 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV557 @ SV706 ) ) @ SV359 ) @ SV121 ) )
= $true )
| ( ( class_Orderings_Oord @ SV706 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7706]) ).
thf(7785,plain,
! [SV128: $i,SV366: $i,SV562: $i,SV710: $i,SV807: $i,SV860: $i] :
( ( ( SV860 = SV807 )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV710 @ SV562 @ SV366 @ SV807 @ SV128 ) @ SV860 )
= SV128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7710]) ).
thf(7786,plain,
! [SV128: $i,SV366: $i,SV562: $i,SV710: $i,SV807: $i,SV860: $i] :
( ( ( SV860 != SV807 )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV710 @ SV562 @ SV366 @ SV807 @ SV128 ) @ SV860 )
= ( hAPP @ SV366 @ SV860 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7711]) ).
thf(7787,plain,
! [SV565: $i,SV131: $i,SV713: $i,SV369: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV713 ) @ SV131 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV565 ) @ SV131 ) )
= $true )
| ( ( SV713 = SV565 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7713]) ).
thf(7788,plain,
! [SV713: $i,SV131: $i,SV565: $i,SV369: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV565 ) @ SV131 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV369 ) @ SV713 ) @ SV131 ) )
= $true )
| ( ( SV713 = SV565 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7714]) ).
thf(7789,plain,
! [SV575: $i,SV810: $i,SV862: $i,SV142: $i,SV380: $i,SV720: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV720 @ SV380 ) @ SV142 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV862 @ ( tc_fun @ SV810 @ tc_HOL_Obool ) ) ) @ SV720 ) @ SV575 ) @ SV380 ) @ SV142 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7716]) ).
thf(7790,plain,
! [SV720: $i,SV810: $i,SV862: $i,SV142: $i,SV380: $i,SV575: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV575 @ SV380 ) @ SV142 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV862 @ ( tc_fun @ SV810 @ tc_HOL_Obool ) ) ) @ SV720 ) @ SV575 ) @ SV380 ) @ SV142 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7717]) ).
thf(7791,plain,
! [SV382: $i,SV577: $i,SV144: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV577 ) @ SV382 ) )
= $true )
| ( ( SV577 = SV382 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7718]) ).
thf(7792,plain,
! [SV577: $i,SV382: $i,SV144: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV382 ) @ SV577 ) )
= $true )
| ( ( SV577 = SV382 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7719]) ).
thf(7793,plain,
! [SV382: $i,SV577: $i,SV144: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV577 ) @ SV382 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV382 ) @ SV577 ) ) )
= $true )
| ( ( SV577 = SV382 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7720]) ).
thf(7794,plain,
! [SV152: $i,SV585: $i,SV813: $i,SV863: $i,SV390: $i,SV727: $i] :
( ( ( SV727 = SV390 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV863 @ SV813 ) @ SV727 ) @ SV585 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV863 @ SV813 ) @ SV390 ) @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7721]) ).
thf(7795,plain,
! [SV390: $i,SV727: $i,SV813: $i,SV863: $i,SV152: $i,SV585: $i] :
( ( ( SV585 = SV152 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV863 @ SV813 ) @ SV727 ) @ SV585 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV863 @ SV813 ) @ SV390 ) @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7722]) ).
thf(7796,plain,
! [SV588: $i,SV155: $i,SV393: $i,SV730: $i,SV814: $i,SV864: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV864 @ SV814 ) @ SV730 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV393 @ ( tc_fun @ SV155 @ tc_HOL_Obool ) ) ) @ SV588 ) @ SV864 ) @ SV814 ) @ SV730 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7723]) ).
thf(7797,plain,
! [SV156: $i,SV394: $i,SV589: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7724]) ).
thf(7798,plain,
! [SV589: $i,SV156: $i,SV394: $i] :
( ( ( SV394 != SV156 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7725]) ).
thf(7799,plain,
! [SV156: $i,SV394: $i,SV589: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
= $false )
| ( ( ~ ( ( SV394 != SV156 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7726]) ).
thf(7800,plain,
! [SV816: $i,SV592: $i,SV160: $i,SV398: $i,SV733: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV398 ) @ SV160 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV592 ) @ SV160 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV733 @ SV592 ) @ SV398 ) )
= $false )
| ( ( c_Predicate_Otransp @ SV816 @ SV733 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7729]) ).
thf(7801,plain,
! [SV407: $i,SV818: $i,SV739: $i,SV169: $i,SV600: $i] :
( ( ( ! [SY2478: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SY2478 ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SY2478 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7732]) ).
thf(7802,plain,
! [SV407: $i,SV818: $i,SV739: $i,SV169: $i,SV600: $i] :
( ( ( ! [SY2479: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SY2479 ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SY2479 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7733]) ).
thf(7803,plain,
! [SV611: $i,SV867: $i,SV884: $i,SV891: $i,SV183: $i,SV421: $i,SV906: $i,SV749: $i,SV824: $i] :
( ( ( ( hAPP @ SV824 @ ( hAPP @ SV749 @ SV906 ) )
= ( hAPP @ SV421 @ ( hAPP @ SV183 @ SV906 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ocomp @ SV891 @ SV884 @ SV867 @ SV824 ) @ SV749 )
= ( hAPP @ ( c_Fun_Ocomp @ SV611 @ SV884 @ SV867 @ SV421 ) @ SV183 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[7736]) ).
thf(7804,plain,
! [SV422: $i,SV899: $i,SV892: $i,SV184: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SV892 ) @ SV899 ) )
| ( ( hAPP @ SV184 @ SV892 )
= ( hAPP @ SV184 @ SV899 ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7737]) ).
thf(7805,plain,
! [SV422: $i,SV899: $i,SV892: $i,SV184: $i] :
( ( ( ~ ( ( ( hAPP @ SV184 @ SV892 )
!= ( hAPP @ SV184 @ SV899 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SV892 ) @ SV899 ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7737]) ).
thf(7806,plain,
! [SV422: $i,SV184: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
| ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
!= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ ( sK8_SY2542 @ SV422 @ SV184 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7738]) ).
thf(7807,plain,
! [SV885: $i,SV893: $i,SV186: $i,SV424: $i,SV613: $i,SV751: $i,SV868: $i,SV826: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV826 @ SV868 ) @ SV751 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV613 @ SV424 @ SV186 @ SV893 @ SV826 ) @ SV885 ) @ SV751 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV893 @ SV885 ) @ SV868 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7739]) ).
thf(7808,plain,
! [SV827: $i,SV187: $i,SV614: $i,SV425: $i,SV752: $i] :
( ( ( ( SV752 != SV425 )
| ( SV614 != SV187 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV752 ) @ SV614 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV425 ) @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7740]) ).
thf(7809,plain,
! [SV827: $i,SV187: $i,SV614: $i,SV425: $i,SV752: $i] :
( ( ( ( SV752 != SV425 )
| ( SV614 != SV187 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV752 ) @ SV614 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV425 ) @ SV187 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7741]) ).
thf(7810,plain,
! [SV907: $i,SV901: $i,SV202: $i,SV440: $i,SV625: $i] :
( ( ( hBOOL @ ( hAPP @ SV625 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV202 ) @ SV901 ) @ SV907 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV625 @ ( sK9_SY2261 @ SV202 @ SV440 @ SV625 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[7742]) ).
thf(7811,plain,
! [SV202: $i,SV440: $i,SV908: $i,SV625: $i] :
( ( ( hBOOL @ ( hAPP @ SV625 @ SV908 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV625 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV202 ) @ ( sK10_SY2264 @ SV202 @ SV440 @ SV625 ) ) @ ( sK11_SY2545 @ SV202 @ SV440 @ SV625 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[7743]) ).
thf(7812,plain,
! [SV441: $i,SV203: $i,SV626: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV203 ) @ SV441 ) ) )
= $true )
| ( ( SV203 = SV441 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV441 ) @ SV203 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV626 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7744]) ).
thf(7813,plain,
! [SV626: $i,SV441: $i,SV203: $i] :
( ( ( SV203 != SV441 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV203 ) @ SV441 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV441 ) @ SV203 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV626 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7745]) ).
thf(7814,plain,
! [SV829: $i,SV869: $i,SV627: $i,SV204: $i,SV442: $i,SV758: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV758 @ SV442 ) @ SV204 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV627 @ SV442 ) @ SV204 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV869 @ ( tc_fun @ SV829 @ tc_HOL_Obool ) ) ) @ SV758 ) @ SV627 ) @ SV442 ) @ SV204 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7746]) ).
thf(7815,plain,
! [SV217: $i,SV638: $i,SV455: $i,SV832: $i,SV764: $i] :
( ( ( ! [SY2491: $i] :
~ ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SY2491 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2491 ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SY2491 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2491 ) @ SV217 ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7752]) ).
thf(7816,plain,
! [SV217: $i,SV638: $i,SV455: $i,SV832: $i,SV764: $i] :
( ( ( ! [SY2492: $i] :
~ ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SY2492 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2492 ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SY2492 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SY2492 ) @ SV217 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7753]) ).
thf(7817,plain,
! [SV834: $i,SV644: $i,SV225: $i,SV463: $i,SV768: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV463 ) @ SV225 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV644 ) @ SV225 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV768 @ SV644 ) @ SV463 ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV834 @ SV768 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7754]) ).
thf(7818,plain,
! [SV226: $i,SV464: $i,SV645: $i,SV769: $i,SV835: $i,SV871: $i,SV886: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) ) )
= $true )
| ( ( ~ ! [SY2430: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SY2430 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2430 ) @ SV226 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7755]) ).
thf(7819,plain,
! [SV835: $i,SV871: $i,SV886: $i,SV226: $i,SV645: $i,SV464: $i,SV769: $i] :
( ( ( ~ ~ ! [SY2431: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SY2431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2431 ) @ SV226 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7756]) ).
thf(7820,plain,
! [SV653: $i,SV776: $i,SV875: $i,SV888: $i,SV235: $i,SV473: $i,SV839: $i] :
( ( ( ~ ( ( ( hAPP @ SV839 @ SV473 )
!= ( hAPP @ SV839 @ SV235 ) )
| ( SV473 = SV235 ) ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV888 @ SV875 @ SV839 @ SV776 @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7758]) ).
thf(7821,plain,
! [SV653: $i,SV776: $i,SV875: $i,SV888: $i,SV839: $i,SV235: $i,SV473: $i] :
( ( ( ~ ( ( SV473 != SV235 )
| ( ( hAPP @ SV839 @ SV473 )
= ( hAPP @ SV839 @ SV235 ) ) ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV888 @ SV875 @ SV839 @ SV776 @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7758]) ).
thf(7822,plain,
! [SV243: $i,SV481: $i,SV660: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) ) )
= $false )
| ( ( SV481 = SV243 )
= $false )
| ( ( class_Orderings_Oorder @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7759]) ).
thf(7823,plain,
! [SV243: $i,SV481: $i,SV660: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) ) )
= $true )
| ( ( SV481 = SV243 )
= $true )
| ( ( class_Orderings_Oorder @ SV660 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7760]) ).
thf(7824,plain,
! [SV69: $i,SV682: $i,SV519: $i,SV308: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ ( sK12_SY1684 @ SV519 @ SV682 @ SV69 @ SV308 ) ) @ SV69 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV682 @ SV519 @ SV308 ) @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7761]) ).
thf(7825,plain,
! [SV519: $i,SV682: $i,SV69: $i,SV902: $i,SV308: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV308 @ SV902 ) @ SV69 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV682 @ SV519 @ SV308 ) @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7762]) ).
thf(7826,plain,
! [SV309: $i,SV70: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK14_SY1062 @ SV309 @ SV70 ) ) @ ( sK14_SY1062 @ SV309 @ SV70 ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[7763]) ).
thf(7827,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) )
| ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SV909 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) )
| ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SV909 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[7764]) ).
thf(7828,plain,
! [SV309: $i,SV910: $i,SV70: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) ) )
= $true )
| ( ( ~ ! [SY1066: $i,SY1067: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[7765]) ).
thf(7829,plain,
! [SV530: $i,SV689: $i,SV86: $i,SV324: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
= $true )
| ( ( SV689 = SV530 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7769]) ).
thf(7830,plain,
! [SV689: $i,SV530: $i,SV86: $i,SV324: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
= $true )
| ( ( SV689 = SV530 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7769]) ).
thf(7831,plain,
! [SV530: $i,SV689: $i,SV86: $i,SV324: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) )
= $true )
| ( ( SV689 = SV530 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7770]) ).
thf(7832,plain,
! [SV689: $i,SV530: $i,SV86: $i,SV324: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) )
= $true )
| ( ( SV689 = SV530 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7770]) ).
thf(7833,plain,
! [SV693: $i,SV535: $i,SV92: $i,SV330: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ ( sK13_SY1733 @ SV535 @ SV693 @ SV92 @ SV330 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV693 @ SV535 @ SV330 ) @ SV92 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7771]) ).
thf(7834,plain,
! [SV535: $i,SV693: $i,SV904: $i,SV92: $i,SV330: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV330 @ SV92 ) @ SV904 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV693 @ SV535 @ SV330 ) @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7772]) ).
thf(7835,plain,
! [SV100: $i,SV338: $i,SV541: $i,SV697: $i,SV797: $i,SV853: $i,SV882: $i,SV890: $i,SV895: $i,SV900: $i,SV905: $i] :
( ( ( ( hAPP @ SV905 @ ( hAPP @ SV900 @ SV895 ) )
!= ( hAPP @ SV890 @ ( hAPP @ SV882 @ SV853 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV797 @ SV697 @ SV541 @ SV905 ) @ SV900 ) @ SV895 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV338 @ SV697 @ SV100 @ SV890 ) @ SV882 ) @ SV853 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7773]) ).
thf(7836,plain,
! [SV114: $i,SV352: $i,SV552: $i,SV703: $i,SV802: $i,SV856: $i] :
( ( ( SV856 = SV802 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV703 @ SV552 @ SV352 @ SV802 @ SV114 ) @ SV856 )
= ( hAPP @ SV352 @ SV856 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7780]) ).
thf(7837,plain,
! [SV803: $i,SV857: $i,SV117: $i,SV554: $i,SV355: $i,SV704: $i] :
( ( ( ( SV704 != SV355 )
| ( SV554 != SV117 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV704 ) @ SV554 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV355 ) @ SV117 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7781]) ).
thf(7838,plain,
! [SV803: $i,SV857: $i,SV117: $i,SV554: $i,SV355: $i,SV704: $i] :
( ( ( ( SV704 != SV355 )
| ( SV554 != SV117 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV704 ) @ SV554 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV355 ) @ SV117 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7782]) ).
thf(7839,plain,
! [SV557: $i,SV121: $i,SV911: $i,SV359: $i,SV706: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV706 ) @ ( hAPP @ SV359 @ SV911 ) ) @ ( hAPP @ SV121 @ SV911 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV557 @ SV706 ) ) @ SV359 ) @ SV121 ) )
= $false )
| ( ( class_Orderings_Oord @ SV706 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[7783]) ).
thf(7840,plain,
! [SV121: $i,SV557: $i,SV359: $i,SV706: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV706 ) @ ( hAPP @ SV359 @ ( sK15_SY2374 @ SV557 @ SV121 @ SV359 @ SV706 ) ) ) @ ( hAPP @ SV121 @ ( sK15_SY2374 @ SV557 @ SV121 @ SV359 @ SV706 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV557 @ SV706 ) ) @ SV359 ) @ SV121 ) )
= $true )
| ( ( class_Orderings_Oord @ SV706 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[7784]) ).
thf(7841,plain,
! [SV128: $i,SV366: $i,SV562: $i,SV710: $i,SV807: $i,SV860: $i] :
( ( ( SV860 = SV807 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV710 @ SV562 @ SV366 @ SV807 @ SV128 ) @ SV860 )
= ( hAPP @ SV366 @ SV860 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7786]) ).
thf(7842,plain,
! [SV577: $i,SV382: $i,SV144: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV382 ) @ SV577 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV144 @ tc_HOL_Obool ) ) @ SV577 ) @ SV382 ) )
= $false )
| ( ( SV577 = SV382 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7793]) ).
thf(7843,plain,
! [SV589: $i,SV156: $i,SV394: $i] :
( ( ( SV394 = SV156 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7798]) ).
thf(7844,plain,
! [SV589: $i,SV156: $i,SV394: $i] :
( ( ( SV394 != SV156 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7799]) ).
thf(7845,plain,
! [SV169: $i,SV739: $i,SV818: $i,SV407: $i,SV600: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ ( sK16_SY2478 @ SV407 @ SV818 @ SV739 @ SV169 @ SV600 ) ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ ( sK16_SY2478 @ SV407 @ SV818 @ SV739 @ SV169 @ SV600 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[7801]) ).
thf(7846,plain,
! [SV407: $i,SV818: $i,SV739: $i,SV169: $i,SV912: $i,SV600: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SV912 ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV912 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[7802]) ).
thf(7847,plain,
! [SV422: $i,SV899: $i,SV892: $i,SV184: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SV892 ) @ SV899 ) )
| ( ( hAPP @ SV184 @ SV892 )
= ( hAPP @ SV184 @ SV899 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7804]) ).
thf(7848,plain,
! [SV422: $i,SV899: $i,SV892: $i,SV184: $i] :
( ( ( ( ( hAPP @ SV184 @ SV892 )
!= ( hAPP @ SV184 @ SV899 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SV892 ) @ SV899 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7805]) ).
thf(7849,plain,
! [SV422: $i,SV184: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
| ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) ) )
= $false )
| ( ( ~ ( ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
!= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ ( sK8_SY2542 @ SV422 @ SV184 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7806]) ).
thf(7850,plain,
! [SV885: $i,SV893: $i,SV186: $i,SV424: $i,SV613: $i,SV751: $i,SV868: $i,SV826: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV826 @ SV868 ) @ SV751 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV613 @ SV424 @ SV186 @ SV893 @ SV826 ) @ SV885 ) @ SV751 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV893 @ SV885 ) @ SV868 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7807]) ).
thf(7851,plain,
! [SV187: $i,SV614: $i,SV827: $i,SV425: $i,SV752: $i] :
( ( ( SV752 != SV425 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV752 ) @ SV614 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV425 ) @ SV187 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7808]) ).
thf(7852,plain,
! [SV425: $i,SV752: $i,SV827: $i,SV187: $i,SV614: $i] :
( ( ( SV614 != SV187 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV752 ) @ SV614 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV425 ) @ SV187 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7808]) ).
thf(7853,plain,
! [SV827: $i,SV187: $i,SV614: $i,SV425: $i,SV752: $i] :
( ( ( SV752 != SV425 )
= $true )
| ( ( SV614 != SV187 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV752 ) @ SV614 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV425 ) @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7809]) ).
thf(7854,plain,
! [SV441: $i,SV203: $i,SV626: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV203 ) @ SV441 ) )
= $false )
| ( ( SV203 = SV441 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV441 ) @ SV203 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV626 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7812]) ).
thf(7855,plain,
! [SV626: $i,SV441: $i,SV203: $i] :
( ( ( SV203 = SV441 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV203 ) @ SV441 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV626 ) @ SV441 ) @ SV203 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV626 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7813]) ).
thf(7856,plain,
! [SV638: $i,SV217: $i,SV455: $i,SV832: $i,SV764: $i] :
( ( ( ~ ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV217 ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[7815]) ).
thf(7857,plain,
! [SV217: $i,SV638: $i,SV913: $i,SV455: $i,SV832: $i,SV764: $i] :
( ( ( ~ ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV913 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV913 ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV913 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV913 ) @ SV217 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[7816]) ).
thf(7858,plain,
! [SV226: $i,SV464: $i,SV645: $i,SV769: $i,SV835: $i,SV871: $i,SV886: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
= $false )
| ( ( ~ ! [SY2430: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SY2430 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2430 ) @ SV226 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7818]) ).
thf(7859,plain,
! [SV835: $i,SV871: $i,SV886: $i,SV226: $i,SV645: $i,SV464: $i,SV769: $i] :
( ( ( ~ ! [SY2431: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SY2431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2431 ) @ SV226 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7819]) ).
thf(7860,plain,
! [SV653: $i,SV776: $i,SV875: $i,SV888: $i,SV235: $i,SV473: $i,SV839: $i] :
( ( ( ( ( hAPP @ SV839 @ SV473 )
!= ( hAPP @ SV839 @ SV235 ) )
| ( SV473 = SV235 ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV888 @ SV875 @ SV839 @ SV776 @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7820]) ).
thf(7861,plain,
! [SV653: $i,SV776: $i,SV875: $i,SV888: $i,SV839: $i,SV235: $i,SV473: $i] :
( ( ( ( SV473 != SV235 )
| ( ( hAPP @ SV839 @ SV473 )
= ( hAPP @ SV839 @ SV235 ) ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV888 @ SV875 @ SV839 @ SV776 @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7821]) ).
thf(7862,plain,
! [SV243: $i,SV481: $i,SV660: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) ) )
= $false )
| ( ( SV481 = SV243 )
= $false )
| ( ( class_Orderings_Oorder @ SV660 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7822]) ).
thf(7863,plain,
! [SV481: $i,SV243: $i,SV660: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) ) )
= $false )
| ( ( SV481 = SV243 )
= $false )
| ( ( class_Orderings_Oorder @ SV660 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7822]) ).
thf(7864,plain,
! [SV243: $i,SV481: $i,SV660: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) ) )
= $true )
| ( ( SV481 = SV243 )
= $true )
| ( ( class_Orderings_Oorder @ SV660 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7823]) ).
thf(7865,plain,
! [SV309: $i,SV70: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK14_SY1062 @ SV309 @ SV70 ) ) @ ( sK14_SY1062 @ SV309 @ SV70 ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7826]) ).
thf(7866,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) )
| ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SV909 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) )
| ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SV909 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7827]) ).
thf(7867,plain,
! [SV309: $i,SV910: $i,SV70: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( ~ ! [SY1066: $i,SY1067: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7828]) ).
thf(7868,plain,
! [SV530: $i,SV689: $i,SV86: $i,SV324: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
= $true )
| ( ( SV689 = SV530 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7829]) ).
thf(7869,plain,
! [SV530: $i,SV689: $i,SV86: $i,SV324: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) )
= $true )
| ( ( SV689 = SV530 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7831]) ).
thf(7870,plain,
! [SV100: $i,SV338: $i,SV541: $i,SV697: $i,SV797: $i,SV853: $i,SV882: $i,SV890: $i,SV895: $i,SV900: $i,SV905: $i] :
( ( ( ( hAPP @ SV905 @ ( hAPP @ SV900 @ SV895 ) )
= ( hAPP @ SV890 @ ( hAPP @ SV882 @ SV853 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV797 @ SV697 @ SV541 @ SV905 ) @ SV900 ) @ SV895 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV338 @ SV697 @ SV100 @ SV890 ) @ SV882 ) @ SV853 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7835]) ).
thf(7871,plain,
! [SV117: $i,SV554: $i,SV803: $i,SV857: $i,SV355: $i,SV704: $i] :
( ( ( SV704 != SV355 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV704 ) @ SV554 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV355 ) @ SV117 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7837]) ).
thf(7872,plain,
! [SV355: $i,SV704: $i,SV803: $i,SV857: $i,SV117: $i,SV554: $i] :
( ( ( SV554 != SV117 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV704 ) @ SV554 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV355 ) @ SV117 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7837]) ).
thf(7873,plain,
! [SV803: $i,SV857: $i,SV117: $i,SV554: $i,SV355: $i,SV704: $i] :
( ( ( SV704 != SV355 )
= $true )
| ( ( SV554 != SV117 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV704 ) @ SV554 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV355 ) @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7838]) ).
thf(7874,plain,
! [SV589: $i,SV156: $i,SV394: $i] :
( ( ( SV394 = SV156 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV589 @ tc_HOL_Obool ) ) @ SV394 ) @ SV156 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7844]) ).
thf(7875,plain,
! [SV169: $i,SV739: $i,SV818: $i,SV407: $i,SV600: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ ( sK16_SY2478 @ SV407 @ SV818 @ SV739 @ SV169 @ SV600 ) ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ ( sK16_SY2478 @ SV407 @ SV818 @ SV739 @ SV169 @ SV600 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7845]) ).
thf(7876,plain,
! [SV407: $i,SV818: $i,SV739: $i,SV169: $i,SV912: $i,SV600: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SV912 ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV912 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7846]) ).
thf(7877,plain,
! [SV422: $i,SV899: $i,SV892: $i,SV184: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SV892 ) @ SV899 ) ) )
= $true )
| ( ( ( hAPP @ SV184 @ SV892 )
= ( hAPP @ SV184 @ SV899 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7847]) ).
thf(7878,plain,
! [SV422: $i,SV899: $i,SV892: $i,SV184: $i] :
( ( ( ( hAPP @ SV184 @ SV892 )
!= ( hAPP @ SV184 @ SV899 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SV892 ) @ SV899 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7848]) ).
thf(7879,plain,
! [SV422: $i,SV184: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ ( sK8_SY2542 @ SV422 @ SV184 ) ) ) )
= $false )
| ( ( ~ ( ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
!= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ ( sK8_SY2542 @ SV422 @ SV184 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7849]) ).
thf(7880,plain,
! [SV422: $i,SV184: $i] :
( ( ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
= $false )
| ( ( ~ ( ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
!= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ ( sK8_SY2542 @ SV422 @ SV184 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7849]) ).
thf(7881,plain,
! [SV187: $i,SV614: $i,SV827: $i,SV425: $i,SV752: $i] :
( ( ( SV752 = SV425 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV752 ) @ SV614 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV425 ) @ SV187 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7851]) ).
thf(7882,plain,
! [SV425: $i,SV752: $i,SV827: $i,SV187: $i,SV614: $i] :
( ( ( SV614 = SV187 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV752 ) @ SV614 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV425 ) @ SV187 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7852]) ).
thf(7883,plain,
! [SV827: $i,SV187: $i,SV614: $i,SV425: $i,SV752: $i] :
( ( ( SV752 = SV425 )
= $false )
| ( ( SV614 != SV187 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV752 ) @ SV614 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV425 ) @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7853]) ).
thf(7884,plain,
! [SV638: $i,SV217: $i,SV455: $i,SV832: $i,SV764: $i] :
( ( ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV217 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7856]) ).
thf(7885,plain,
! [SV217: $i,SV638: $i,SV913: $i,SV455: $i,SV832: $i,SV764: $i] :
( ( ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV913 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV913 ) @ SV638 )
!= SV217 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV913 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV913 ) @ SV217 ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7857]) ).
thf(7886,plain,
! [SV835: $i,SV871: $i,SV886: $i,SV226: $i,SV645: $i,SV464: $i,SV769: $i] :
( ( ( ! [SY2430: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SY2430 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2430 ) @ SV226 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7858]) ).
thf(7887,plain,
! [SV835: $i,SV871: $i,SV886: $i,SV226: $i,SV645: $i,SV464: $i,SV769: $i] :
( ( ( ! [SY2431: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SY2431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SY2431 ) @ SV226 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7859]) ).
thf(7888,plain,
! [SV653: $i,SV776: $i,SV875: $i,SV888: $i,SV235: $i,SV473: $i,SV839: $i] :
( ( ( ( hAPP @ SV839 @ SV473 )
!= ( hAPP @ SV839 @ SV235 ) )
= $true )
| ( ( SV473 = SV235 )
= $true )
| ( ( c_Typedef_Otype__definition @ SV888 @ SV875 @ SV839 @ SV776 @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7860]) ).
thf(7889,plain,
! [SV653: $i,SV776: $i,SV875: $i,SV888: $i,SV839: $i,SV235: $i,SV473: $i] :
( ( ( SV473 != SV235 )
= $true )
| ( ( ( hAPP @ SV839 @ SV473 )
= ( hAPP @ SV839 @ SV235 ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV888 @ SV875 @ SV839 @ SV776 @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7861]) ).
thf(7890,plain,
! [SV243: $i,SV481: $i,SV660: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) )
= $true )
| ( ( SV481 = SV243 )
= $false )
| ( ( class_Orderings_Oorder @ SV660 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7862]) ).
thf(7891,plain,
! [SV481: $i,SV243: $i,SV660: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) )
= $true )
| ( ( SV481 = SV243 )
= $false )
| ( ( class_Orderings_Oorder @ SV660 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7863]) ).
thf(7892,plain,
! [SV243: $i,SV481: $i,SV660: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) ) )
= $true )
| ( ( SV481 = SV243 )
= $true )
| ( ( class_Orderings_Oorder @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7864]) ).
thf(7893,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) )
| ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SV909 ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7866]) ).
thf(7894,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) )
| ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SV909 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7866]) ).
thf(7895,plain,
! [SV309: $i,SV910: $i,SV70: $i] :
( ( ( ! [SY1066: $i,SY1067: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1067 ) @ SY1067 ) ) )
| ( ( hAPP @ SV70 @ SY1066 )
!= ( hAPP @ SV70 @ SY1067 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY1066 ) @ SY1067 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7867]) ).
thf(7896,plain,
! [SV530: $i,SV689: $i,SV86: $i,SV324: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
= $true )
| ( ( SV689 = SV530 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7868]) ).
thf(7897,plain,
! [SV530: $i,SV689: $i,SV86: $i,SV324: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV689 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV86 ) @ SV530 ) )
= $true )
| ( ( SV689 = SV530 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7869]) ).
thf(7898,plain,
! [SV117: $i,SV554: $i,SV803: $i,SV857: $i,SV355: $i,SV704: $i] :
( ( ( SV704 = SV355 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV704 ) @ SV554 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV355 ) @ SV117 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7871]) ).
thf(7899,plain,
! [SV355: $i,SV704: $i,SV803: $i,SV857: $i,SV117: $i,SV554: $i] :
( ( ( SV554 = SV117 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV704 ) @ SV554 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV355 ) @ SV117 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7872]) ).
thf(7900,plain,
! [SV803: $i,SV857: $i,SV117: $i,SV554: $i,SV355: $i,SV704: $i] :
( ( ( SV704 = SV355 )
= $false )
| ( ( SV554 != SV117 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV704 ) @ SV554 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV355 ) @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7873]) ).
thf(7901,plain,
! [SV169: $i,SV739: $i,SV818: $i,SV407: $i,SV600: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ ( sK16_SY2478 @ SV407 @ SV818 @ SV739 @ SV169 @ SV600 ) ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ ( sK16_SY2478 @ SV407 @ SV818 @ SV739 @ SV169 @ SV600 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7875]) ).
thf(7902,plain,
! [SV407: $i,SV818: $i,SV739: $i,SV169: $i,SV912: $i,SV600: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SV912 ) @ SV169 ) )
| ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV912 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7876]) ).
thf(7903,plain,
! [SV422: $i,SV899: $i,SV892: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SV892 ) @ SV899 ) )
= $false )
| ( ( ( hAPP @ SV184 @ SV892 )
= ( hAPP @ SV184 @ SV899 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7877]) ).
thf(7904,plain,
! [SV422: $i,SV899: $i,SV892: $i,SV184: $i] :
( ( ( ( hAPP @ SV184 @ SV892 )
= ( hAPP @ SV184 @ SV899 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ SV892 ) @ SV899 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7878]) ).
thf(7905,plain,
! [SV422: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
!= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ ( sK8_SY2542 @ SV422 @ SV184 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7879]) ).
thf(7906,plain,
! [SV422: $i,SV184: $i] :
( ( ( ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
!= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ ( sK8_SY2542 @ SV422 @ SV184 ) ) ) )
= $false )
| ( ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7880]) ).
thf(7907,plain,
! [SV827: $i,SV425: $i,SV752: $i,SV187: $i,SV614: $i] :
( ( ( SV614 = SV187 )
= $false )
| ( ( SV752 = SV425 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV752 ) @ SV614 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV827 ) @ SV425 ) @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7883]) ).
thf(7908,plain,
! [SV638: $i,SV217: $i,SV455: $i,SV832: $i,SV764: $i] :
( ( ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV638 )
!= SV217 ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV217 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7884]) ).
thf(7909,plain,
! [SV217: $i,SV638: $i,SV913: $i,SV455: $i,SV832: $i,SV764: $i] :
( ( ( ~ ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV913 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV913 ) @ SV638 )
!= SV217 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7885]) ).
thf(7910,plain,
! [SV217: $i,SV638: $i,SV455: $i,SV913: $i,SV764: $i,SV832: $i] :
( ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV913 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV913 ) @ SV217 ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7885]) ).
thf(7911,plain,
! [SV645: $i,SV226: $i,SV886: $i,SV871: $i,SV835: $i,SV464: $i,SV769: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ ( sK18_SY2430 @ SV835 @ SV871 @ SV886 @ SV226 @ SV645 @ SV464 @ SV769 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ ( sK18_SY2430 @ SV835 @ SV871 @ SV886 @ SV226 @ SV645 @ SV464 @ SV769 ) ) @ SV226 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[7886]) ).
thf(7912,plain,
! [SV835: $i,SV871: $i,SV886: $i,SV226: $i,SV645: $i,SV914: $i,SV464: $i,SV769: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SV914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SV914 ) @ SV226 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[7887]) ).
thf(7913,plain,
! [SV653: $i,SV776: $i,SV875: $i,SV888: $i,SV235: $i,SV473: $i,SV839: $i] :
( ( ( ( hAPP @ SV839 @ SV473 )
= ( hAPP @ SV839 @ SV235 ) )
= $false )
| ( ( SV473 = SV235 )
= $true )
| ( ( c_Typedef_Otype__definition @ SV888 @ SV875 @ SV839 @ SV776 @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7888]) ).
thf(7914,plain,
! [SV653: $i,SV776: $i,SV875: $i,SV888: $i,SV839: $i,SV235: $i,SV473: $i] :
( ( ( SV473 = SV235 )
= $false )
| ( ( ( hAPP @ SV839 @ SV473 )
= ( hAPP @ SV839 @ SV235 ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV888 @ SV875 @ SV839 @ SV776 @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7889]) ).
thf(7915,plain,
! [SV481: $i,SV243: $i,SV660: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV243 ) @ SV481 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV660 ) @ SV481 ) @ SV243 ) )
= $false )
| ( ( SV481 = SV243 )
= $true )
| ( ( class_Orderings_Oorder @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7892]) ).
thf(7916,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) )
| ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SV909 ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7893]) ).
thf(7917,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) )
| ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SV909 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7894]) ).
thf(7918,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ! [SY2549: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ SY2549 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY2549 ) @ SY2549 ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ SY2549 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SY2549 ) @ SY2549 ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ SY2549 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ SY2549 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[7895]) ).
thf(7919,plain,
! [SV803: $i,SV857: $i,SV355: $i,SV704: $i,SV117: $i,SV554: $i] :
( ( ( SV554 = SV117 )
= $false )
| ( ( SV704 = SV355 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV704 ) @ SV554 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV857 @ SV803 ) @ SV355 ) @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7900]) ).
thf(7920,plain,
! [SV169: $i,SV739: $i,SV818: $i,SV407: $i,SV600: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ ( sK16_SY2478 @ SV407 @ SV818 @ SV739 @ SV169 @ SV600 ) ) @ SV169 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7901]) ).
thf(7921,plain,
! [SV169: $i,SV407: $i,SV818: $i,SV600: $i,SV739: $i] :
( ( ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ ( sK16_SY2478 @ SV407 @ SV818 @ SV739 @ SV169 @ SV600 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7901]) ).
thf(7922,plain,
! [SV407: $i,SV818: $i,SV739: $i,SV169: $i,SV912: $i,SV600: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SV912 ) @ SV169 ) ) )
= $true )
| ( ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV912 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7902]) ).
thf(7923,plain,
! [SV422: $i,SV184: $i] :
( ( ( ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
!= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ ( sK8_SY2542 @ SV422 @ SV184 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7905]) ).
thf(7924,plain,
! [SV422: $i,SV184: $i] :
( ( ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
!= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
= $false )
| ( ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7906]) ).
thf(7925,plain,
! [SV422: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
= $false )
| ( ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7906]) ).
thf(7926,plain,
! [SV638: $i,SV217: $i,SV455: $i,SV832: $i,SV764: $i] :
( ( ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV638 )
!= SV217 ) )
= $false )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV217 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7908]) ).
thf(7927,plain,
! [SV217: $i,SV638: $i,SV913: $i,SV455: $i,SV832: $i,SV764: $i] :
( ( ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV913 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV913 ) @ SV638 )
!= SV217 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7909]) ).
thf(7928,plain,
! [SV217: $i,SV638: $i,SV455: $i,SV913: $i,SV764: $i,SV832: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV913 )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV913 ) @ SV217 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7910]) ).
thf(7929,plain,
! [SV645: $i,SV226: $i,SV886: $i,SV871: $i,SV835: $i,SV464: $i,SV769: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ ( sK18_SY2430 @ SV835 @ SV871 @ SV886 @ SV226 @ SV645 @ SV464 @ SV769 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ ( sK18_SY2430 @ SV835 @ SV871 @ SV886 @ SV226 @ SV645 @ SV464 @ SV769 ) ) @ SV226 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7911]) ).
thf(7930,plain,
! [SV835: $i,SV871: $i,SV886: $i,SV226: $i,SV645: $i,SV914: $i,SV464: $i,SV769: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SV914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SV914 ) @ SV226 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7912]) ).
thf(7931,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) )
| ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SV909 ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7916]) ).
thf(7932,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) )
| ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SV909 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7917]) ).
thf(7933,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[7918]) ).
thf(7934,plain,
! [SV169: $i,SV739: $i,SV818: $i,SV407: $i,SV600: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ ( sK16_SY2478 @ SV407 @ SV818 @ SV739 @ SV169 @ SV600 ) ) @ SV169 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7920]) ).
thf(7935,plain,
! [SV169: $i,SV407: $i,SV818: $i,SV600: $i,SV739: $i] :
( ( ( SV739
= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ ( sK16_SY2478 @ SV407 @ SV818 @ SV739 @ SV169 @ SV600 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7921]) ).
thf(7936,plain,
! [SV407: $i,SV818: $i,SV739: $i,SV169: $i,SV912: $i,SV600: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SV912 ) @ SV169 ) )
= $false )
| ( ( SV739
!= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV912 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7922]) ).
thf(7937,plain,
! [SV422: $i,SV184: $i] :
( ( ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
!= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7923]) ).
thf(7938,plain,
! [SV422: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7923]) ).
thf(7939,plain,
! [SV422: $i,SV184: $i] :
( ( ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
= $true )
| ( ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7924]) ).
thf(7940,plain,
! [SV638: $i,SV217: $i,SV455: $i,SV832: $i,SV764: $i] :
( ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) )
= $false )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV217 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7926]) ).
thf(7941,plain,
! [SV764: $i,SV455: $i,SV638: $i,SV217: $i,SV832: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV638 )
!= SV217 )
= $false )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV217 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7926]) ).
thf(7942,plain,
! [SV217: $i,SV638: $i,SV913: $i,SV455: $i,SV832: $i,SV764: $i] :
( ( ( SV764
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV913 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV913 ) @ SV638 )
!= SV217 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7927]) ).
thf(7943,plain,
! [SV217: $i,SV638: $i,SV455: $i,SV913: $i,SV764: $i,SV832: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV913 )
!= SV455 )
= $true )
| ( ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV913 ) @ SV217 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7928]) ).
thf(7944,plain,
! [SV645: $i,SV226: $i,SV886: $i,SV871: $i,SV835: $i,SV464: $i,SV769: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ ( sK18_SY2430 @ SV835 @ SV871 @ SV886 @ SV226 @ SV645 @ SV464 @ SV769 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ ( sK18_SY2430 @ SV835 @ SV871 @ SV886 @ SV226 @ SV645 @ SV464 @ SV769 ) ) @ SV226 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7929]) ).
thf(7945,plain,
! [SV835: $i,SV871: $i,SV886: $i,SV226: $i,SV645: $i,SV914: $i,SV464: $i,SV769: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SV914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SV914 ) @ SV226 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7930]) ).
thf(7946,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) )
| ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SV909 ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7931]) ).
thf(7947,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) )
| ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SV909 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7932]) ).
thf(7948,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7933]) ).
thf(7949,plain,
! [SV169: $i,SV912: $i,SV407: $i,SV818: $i,SV600: $i,SV739: $i] :
( ( ( SV739
= ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV912 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) @ SV912 ) @ SV169 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV818 @ tc_HOL_Obool ) ) @ SV739 ) @ ( hAPP @ ( c_Set_Oimage @ SV600 @ SV818 @ SV407 ) @ SV169 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7936]) ).
thf(7950,plain,
! [SV422: $i,SV184: $i] :
( ( ( ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) )
= ( hAPP @ SV184 @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV184 @ ( sK3_SY1425 @ SV422 @ SV184 ) ) @ ( sK8_SY2542 @ SV422 @ SV184 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV422 @ SV184 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7937]) ).
thf(7951,plain,
! [SV638: $i,SV217: $i,SV455: $i,SV832: $i,SV764: $i] :
( ( ( SV764
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV217 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7940]) ).
thf(7952,plain,
! [SV764: $i,SV455: $i,SV638: $i,SV217: $i,SV832: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV638 )
= SV217 )
= $true )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV217 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7941]) ).
thf(7953,plain,
! [SV217: $i,SV638: $i,SV913: $i,SV455: $i,SV832: $i,SV764: $i] :
( ( ( SV764
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV913 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV913 ) @ SV638 )
!= SV217 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7942]) ).
thf(7954,plain,
! [SV217: $i,SV638: $i,SV455: $i,SV913: $i,SV764: $i,SV832: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV913 )
= SV455 )
= $false )
| ( ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV913 ) @ SV217 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7943]) ).
thf(7955,plain,
! [SV645: $i,SV226: $i,SV886: $i,SV871: $i,SV835: $i,SV464: $i,SV769: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ ( sK18_SY2430 @ SV835 @ SV871 @ SV886 @ SV226 @ SV645 @ SV464 @ SV769 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7944]) ).
thf(7956,plain,
! [SV769: $i,SV464: $i,SV226: $i,SV886: $i,SV871: $i,SV835: $i,SV645: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ ( sK18_SY2430 @ SV835 @ SV871 @ SV886 @ SV226 @ SV645 @ SV464 @ SV769 ) ) @ SV226 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7944]) ).
thf(7957,plain,
! [SV835: $i,SV871: $i,SV886: $i,SV226: $i,SV645: $i,SV914: $i,SV464: $i,SV769: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SV914 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SV914 ) @ SV226 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7945]) ).
thf(7958,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) )
| ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SV909 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7946]) ).
thf(7959,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) )
| ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SV909 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7947]) ).
thf(7960,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7948]) ).
thf(7961,plain,
! [SV455: $i,SV638: $i,SV217: $i,SV764: $i,SV832: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV217 ) ) )
= $false )
| ( ( SV764
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7951]) ).
thf(7962,plain,
! [SV455: $i,SV638: $i,SV217: $i,SV764: $i,SV832: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) )
!= SV455 )
| ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV217 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV638 )
= SV217 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7952]) ).
thf(7963,plain,
! [SV455: $i,SV764: $i,SV217: $i,SV638: $i,SV913: $i,SV832: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV913 ) @ SV638 )
= SV217 )
= $false )
| ( ( SV764
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV913 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7953]) ).
thf(7964,plain,
! [SV455: $i,SV764: $i,SV217: $i,SV913: $i,SV832: $i,SV638: $i] :
( ( ( SV638
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV913 ) @ SV217 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV913 )
= SV455 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7954]) ).
thf(7965,plain,
! [SV645: $i,SV226: $i,SV886: $i,SV871: $i,SV835: $i,SV464: $i,SV769: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ ( sK18_SY2430 @ SV835 @ SV871 @ SV886 @ SV226 @ SV645 @ SV464 @ SV769 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7955]) ).
thf(7966,plain,
! [SV769: $i,SV464: $i,SV226: $i,SV886: $i,SV871: $i,SV835: $i,SV645: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ ( sK18_SY2430 @ SV835 @ SV871 @ SV886 @ SV226 @ SV645 @ SV464 @ SV769 ) ) @ SV226 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7956]) ).
thf(7967,plain,
! [SV835: $i,SV871: $i,SV886: $i,SV226: $i,SV645: $i,SV914: $i,SV464: $i,SV769: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SV914 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SV914 ) @ SV226 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7957]) ).
thf(7968,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7958]) ).
thf(7969,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SV909 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7958]) ).
thf(7970,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) ) )
= $true )
| ( ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SV909 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7959]) ).
thf(7971,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7960]) ).
thf(7972,plain,
! [SV455: $i,SV638: $i,SV217: $i,SV764: $i,SV832: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) )
!= SV455 )
= $false )
| ( ( SV764
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7961]) ).
thf(7973,plain,
! [SV764: $i,SV455: $i,SV217: $i,SV832: $i,SV638: $i] :
( ( ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV217 ) )
= $false )
| ( ( SV764
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7961]) ).
thf(7974,plain,
! [SV455: $i,SV638: $i,SV217: $i,SV764: $i,SV832: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) )
!= SV455 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV638 )
= SV217 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7962]) ).
thf(7975,plain,
! [SV764: $i,SV455: $i,SV217: $i,SV832: $i,SV638: $i] :
( ( ( SV638
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV217 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV638 )
= SV217 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7962]) ).
thf(7976,plain,
! [SV835: $i,SV871: $i,SV886: $i,SV464: $i,SV769: $i,SV226: $i,SV914: $i,SV645: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV645 @ SV914 ) @ SV226 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV769 @ SV464 ) @ SV914 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV886 @ SV871 @ SV835 @ SV769 @ SV645 ) @ SV464 ) @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7967]) ).
thf(7977,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7968]) ).
thf(7978,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ( hAPP @ SV70 @ SV903 )
= ( hAPP @ SV70 @ SV909 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7969]) ).
thf(7979,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) ) )
= $false )
| ( ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SV909 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7970]) ).
thf(7980,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7971]) ).
thf(7981,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7971]) ).
thf(7982,plain,
! [SV455: $i,SV638: $i,SV217: $i,SV764: $i,SV832: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) )
= SV455 )
= $true )
| ( ( SV764
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7972]) ).
thf(7983,plain,
! [SV764: $i,SV455: $i,SV217: $i,SV832: $i,SV638: $i] :
( ( ( SV638
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV217 ) )
= $true )
| ( ( SV764
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7973]) ).
thf(7984,plain,
! [SV455: $i,SV638: $i,SV217: $i,SV764: $i,SV832: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) )
= SV455 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV638 )
= SV217 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7974]) ).
thf(7985,plain,
! [SV764: $i,SV455: $i,SV217: $i,SV832: $i,SV638: $i] :
( ( ( SV638
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV217 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ ( sK17_SY2491 @ SV217 @ SV638 @ SV455 @ SV832 @ SV764 ) ) @ SV638 )
= SV217 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV764 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV832 ) @ SV455 ) @ SV217 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7975]) ).
thf(7986,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7977]) ).
thf(7987,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) )
= $true )
| ( ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SV909 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7979]) ).
thf(7988,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7980]) ).
thf(7989,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7981]) ).
thf(7990,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7986]) ).
thf(7991,plain,
! [SV309: $i,SV903: $i,SV909: $i,SV70: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7986]) ).
thf(7992,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) )
= $true )
| ( ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SV909 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7987]) ).
thf(7993,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7988]) ).
thf(7994,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $true )
| ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7989]) ).
thf(7995,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7990]) ).
thf(7996,plain,
! [SV309: $i,SV903: $i,SV909: $i,SV70: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7991]) ).
thf(7997,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) ) )
= $true )
| ( ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SV909 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7992]) ).
thf(7998,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7993]) ).
thf(7999,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7993]) ).
thf(8000,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $false )
| ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7994]) ).
thf(8001,plain,
! [SV309: $i,SV903: $i,SV909: $i,SV70: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
= $false )
| ( ( ( hAPP @ SV70 @ SV903 )
!= ( hAPP @ SV70 @ SV909 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7997]) ).
thf(8002,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7998]) ).
thf(8003,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
= $true )
| ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8000]) ).
thf(8004,plain,
! [SV309: $i,SV909: $i,SV903: $i,SV70: $i] :
( ( ( ( hAPP @ SV70 @ SV903 )
= ( hAPP @ SV70 @ SV909 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV903 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV909 ) @ SV909 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV903 ) @ SV909 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8001]) ).
thf(8005,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8002]) ).
thf(8006,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
= $true )
| ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8003]) ).
thf(8007,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8005]) ).
thf(8008,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8005]) ).
thf(8009,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
= $true )
| ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8006]) ).
thf(8010,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8007]) ).
thf(8011,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8008]) ).
thf(8012,plain,
! [SV309: $i,SV910: $i,SV70: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
= $false )
| ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8009]) ).
thf(8013,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8010]) ).
thf(8014,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8012]) ).
thf(8015,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8013]) ).
thf(8016,plain,
! [SV309: $i,SV910: $i,SV70: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8013]) ).
thf(8017,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
= $false )
| ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8014]) ).
thf(8018,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8015]) ).
thf(8019,plain,
! [SV309: $i,SV910: $i,SV70: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8016]) ).
thf(8020,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
= $false )
| ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8017]) ).
thf(8021,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
= $false )
| ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8017]) ).
thf(8022,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
= $false )
| ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8020]) ).
thf(8023,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
| ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
= $false )
| ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8022]) ).
thf(8024,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
= $false )
| ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8023]) ).
thf(8025,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
!= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
= $false )
| ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8023]) ).
thf(8026,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
= $false )
| ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8024]) ).
thf(8027,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
= $false )
| ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8025]) ).
thf(8028,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
= $false )
| ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8026]) ).
thf(8029,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
= $false )
| ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8028]) ).
thf(8030,plain,
! [SV309: $i,SV910: $i,SV70: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
= $false )
| ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8028]) ).
thf(8031,plain,
! [SV910: $i,SV309: $i,SV70: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
= $false )
| ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8029]) ).
thf(8032,plain,
! [SV309: $i,SV910: $i,SV70: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) ) )
= $false )
| ( ( ( hAPP @ SV70 @ ( sK19_SY1066 @ SV309 @ SV910 @ SV70 ) )
= ( hAPP @ SV70 @ ( sK20_SY2549 @ SV910 @ SV309 @ SV70 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV70 @ SV910 ) @ SV910 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV309 @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8030]) ).
thf(8033,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[5496,8032,8031,8027,8021,8019,8018,8011,8004,7999,7996,7995,7985,7984,7983,7982,7978,7976,7966,7965,7964,7963,7950,7949,7939,7938,7935,7934,7925,7919,7915,7914,7913,7907,7904,7903,7899,7898,7897,7896,7891,7890,7882,7881,7874,7870,7865,7855,7854,7850,7843,7842,7841,7840,7839,7836,7834,7833,7832,7830,7825,7824,7817,7814,7811,7810,7803,7800,7797,7796,7795,7794,7792,7791,7790,7789,7788,7787,7785,7779,7778,7777,7776,7775,7774,7768,7767,7766,7757,7751,7750,7749,7748,7747,7735,7734,7731,7730,7728,7727,7715,7712,7709,7708,7707,7700,7697,7696,7694,7690,7689,7686,7683,7682,7671,7670,7668,7667,7665,7650,7649,7640,7639,7638,7633,7627,7624,7620,7619,7614,7613,7610,7608,7603,7602,7601,7586,7583,7577,7566,7561,7558,7557,7553,7552,7551,7550,7549,7544,7537,7536,7534,7533,7532,7530,7519,7518,7517,7515,7511,7508,7507,7500,7499,7496,7495,7492,7490,7489,7488,7487,7486,7466,7463,7460,7452,7451,7450,7446,7442,7441,7438,7435,7434,7424,7423,7422,7419,7418,7417,7400,7393,7391,7390,7388,7381,7380,7370,7366,7365,7362,7356,7349,7348,7334,7332,7325,7324,7323,7298,7291,7290,7279,7278,7271,7270,7265,7251,7250,7246,7202,7188,7182,7171,7162,7129,7094,7084,7081,7079,7078,7077,7076,7075,7073,7071,7064,7048,7036,7023,7020,6999,6974,6966,6965,6950,6947,6934,6929,6921,6916,6903,6902,6888,6886,6881,6879,6875,6863,6853,6842,6841,6837,6825,6824,6818,6804,6803,6785,6732,6731,6718,6706,6704,6702,6696,6685,6683,6682,6681,6680,6678,6677,6676,6672,6671,6669,6662,6661,6660,6659,6658,6657,6475,6458,6452,6451,6448,6447,6446,6445,6443,6442,6441,6440,6435,6434,6433,6432,6431,6263,6234,6233,6227,6226,6225,6199,6198,6197,6196,6195,6194,6193,6192,6191,6009,5997,5990,5975,5973,5762,5750,5740,5739,5738,5737,5736,5735,5734,5733,5732,5731,5730,5729,5728,5727,5726,5725,5724,5723,5708]) ).
thf(8034,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[8033]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW311+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.19 % Computer : n010.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 16:53:25 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 138.14/28.19 .....................................
% 138.14/28.19
% 138.14/28.19 No.of.Axioms: 266
% 138.14/28.19
% 138.14/28.19 Length.of.Defs: 0
% 138.14/28.19
% 138.14/28.19 Contains.Choice.Funs: false
% 138.14/28.19 .........................................................................................................................................................................................................
% 138.14/28.19
% 138.14/28.19 ********************************
% 138.14/28.19 * All subproblems solved! *
% 138.14/28.19 ********************************
% 138.14/28.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:267,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:289,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:8033,loop_count:0,foatp_calls:1,translation:fof_full)
% 138.14/28.19
% 138.14/28.19 %**** Beginning of derivation protocol ****
% 138.14/28.19 % SZS output start CNFRefutation
% See solution above
% 28.03/28.23
% 28.03/28.23 %**** End of derivation protocol ****
% 28.03/28.23 %**** no. of clauses in derivation: 3078 ****
% 28.03/28.23 %**** clause counter: 8033 ****
% 28.03/28.23
% 28.03/28.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:267,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:289,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:8033,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------